Answer:
5. there was a: 18% decrease.
6. if the intial value was 285 and there was a 15 difference then the final value is 300. The change is 5.26%.
7. She has a 33.3333 % increase
8. The amount of students increased by 23.0769%
I hope this somewhat helps
Determine the prime factorization of 36
a) 2² x 9
b) 4 x 9
c) 6²
d) 2² x 3²
Suppose the line contains the points (4,0) and (0,-2). If x = 3, find y.
The line which contains the points (4,0) and (0,-2), value of y when x =3 is, -1/2
What is the equation of line?The equation of a straight line is a relationship between x and y coordinates, The two point form of a straight line is y-y₁ = y₂-y₁/x₂-x₁(x-x₁).
Given that,
The points, (4,0) and (0,-2)
Equation of line for given two points,
y-y₁ = y₂-y₁/x₂-x₁(x-x₁)
y-0 = -2 - 0/0-4(x-4)
y = 1/2(x - 4)
2y = x - 4
when x = 3,
y = 1/2(3 - 4)
y = - 1/2
Hence, the value of y is -1/2
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What is the new equation if you first shift by 4 units to the right and then compress horizontally by a factor of 2 ? (Express numbers in exact form. Use symbolic notation and fractions where needed.) Suppose that the graph of f(x)=x 4
−x 2
is compressed horizontally by a factor of 2 and is then shifted 4 units to the right. What is the equation of this new graph? (Express numbers in exact form. Use symbolic notation and fractions where needed.) y 2
(x)= y 1
(x)= Graph both y=f(x) and y=y 2
(x) using the graphing utility. Separate each expression with a comma to graph both curves on the same axes.
The equation of the new graph obtained by compressing the graph of y = f(x) horizontally by a factor of 2 and shifting it 4 units to the right is given by
y 2(x) = f(2(x - 4)) or y 2(x) = (2(x - 4))4 - (2(x - 4))2.
To obtain the new equation of the graph after compressing the graph of y = f(x) horizontally by a factor of 2 and shifting it 4 units to the right, it is necessary to:
Substitute x - 4 for x, which implies that x = (1/2)(x' + 4),
where x' is the horizontal coordinate of the new point.
Thus, substituting into the equation of the graph, we have:
y 2(x) = f(2(x - 4))
= 2(x - 4)4 - 2(x - 4)2
= 2[(1/2)(x' + 4) - 4]4 - 2[(1/2)(x' + 4) - 4]2
= (x' - 4)4 - (x' - 4)2
= x'4 - 8x'3 + 24x'2 - 32x' + 16
Therefore, the equation of the new graph obtained by compressing the graph of y = f(x) horizontally by a factor of 2 and shifting it 4 units to the right is y 2(x) = x'4 - 8x'3 + 24x'2 - 32x' + 16,
where x' is the horizontal coordinate of the new point.
Graph of y = f(x) and y = y 2(x):
\(y_1(x) = x^4 - x^2\)\(y_2(x) = \frac{1}{16} (2x-8)^4 - \frac{1}{4} (2x-8)^2 + 1\)
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What is the result when the number 31 is increased by 8% round your answer to the nearest 10th
The result when the number 31 is increased by 8% and rounded to the nearest tenth is 33.5.
To find the result when the number 31 is increased by 8%, we can calculate 8% of 31 and add it to 31.
8% of 31 can be found by multiplying 31 by 0.08:
8% of 31 = 31 * 0.08 = 2.48
Now, we add this result to 31:
31 + 2.48 = 33.48
Rounding this answer to the nearest tenth, we get:
33.5
Therefore, the result when the number 31 is increased by 8% and rounded to the nearest tenth is 33.5.
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I really need help with rotations, translations, dilutions, scale factor, reflections, basically transformations? I need help with these on the graph. Please hurry! Thank you so much!
Explanation:
The figure preserves its size in certain transformations and only its location is changed. Examples of this kind of transformation are: translations, rotations, and reflections. The size of the figure can change with other transformations, such as dilations.
A translation is a transition that slides through a plane or through space through a figure. Both points of a diagram travel the same distance and the same direction as a translation. A TRANSLATION IS A CHANGE IN LOCATION. A translation is usually specified by a direction and a distance.
A rotation is a move that transforms a figure around a point or a line (around). Rotation involves simply rotating a shape. The center of rotation is called the point at which a figure revolves. The rotation center may be on or outside of the shape. What seems like a rotation? Rotation Core A ROTATION Implies TO Transform A FIGURE.
A transformation that flips a figure over a line is a mirror. A REFLECTION IS FLIPPED OVER A LINE. Note, it's the same but it looks like a mirror image of itself when a shape is mirrored. Remember, the line that forms a shape is flipped precisely over the same distance that is considered a line from the reflection. Reflection line on both ends. It is possible to reflect on the outline or it may be outside the shape.
Without modifying the shape, dilation shifts the scale of the shape. When you go to the eye specialist, your pupils are dilated. Let's try it by shutting the lights off. Dilations are created as you enlarge a photograph or use a copy machine to minimize a map. To render a shape larger, Widen means. Reducing involves having a shape smaller.
The scale factor shows you how much you enlarge or decrease something.
Hope this helps :D (paraphrased; no plagiarism)
what is the equation of the quadratic function that has x intercepts of -2 and 9?
Answer:
f(x) = (x - 9)(x + 2) = x^2 - 7x - 18
Step-by-step explanation:
If the x-intercepts are -2 and 9, then the factors of this quadratic are (x + 2) and (x - 9). Multiplying these two factors together, we get:
f(x) = (x - 9)(x + 2) = x^2 - 9x + 2x -18, or
f(x) = (x - 9)(x + 2) = x^2 - 7x - 18
If you are given the length of a hypotenuse and the length of an adjacent side, what
trigonometry ratio could you use.
tangent
cosine
trigonometry
sine
Answer:
cosine
Step-by-step explanation:
Dan has 4 over 5 cup of ice cream. How many 1 over 8 -cup servings are in 4 over 5 cup of ice cream?
A. 6 and 2 over 5
B. 6 and 1 over 2
C. 8 and 2 over 5
D. 8 and 1 over 2
Answer:
it is A
Step-by-step explanation:
you have to do Keep Change Flip on the step one that's on the picture 4 * 8 equals 32 five of the nominator * 1 equals 5 the answer is 32/5 they are asking another way to explain this answer. 6 2/5 is the answer because 5 times 6 =30 plus 2 thats on the top = 32/5
from 2005 to 2018, the annual investment in renewable energy sources in the united states increased from $11.4 billion to $46.5 billion. calculate the percent change in renewable energy investment in the us from 2005 to 2018.
To calculate the percent change in renewable energy investment in the US from 2005 to 2018, you can use the following formula:
Percent change = ((Final value - Initial value) / Initial value) * 100%
In this case, the initial value is $11.4 billion in 2005 and the final value is $46.5 billion in 2018. Plugging these values into the formula, we get:
Percent change = (($46.5 billion - $11.4 billion) / $11.4 billion) * 100%
= ($35.1 billion / $11.4 billion) * 100%
= 3.085 * 100%
= 308.5%
So, the percent change in renewable energy investment in the US from 2005 to 2018 was 308.5%, a substantial increase over the 13-year period.
find the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π3.
To find the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3, we first need to compute the derivative of the function.
f(x) = ln(4sec(x))
f'(x) = (1/sec(x)) * (4sec(x)) * tan(x) = 4tan(x)
Next, we use the arc length formula:
L = ∫ [a,b] √[1 + (f'(x))^2] dx
Substituting in the values, we get:
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
We can simplify this by using the identity 1 + tan^2(x) = sec^2(x):
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
= ∫ [0,π/3] √[1 + 16tan^2(x)] dx
= ∫ [0,π/3] √[sec^2(x) + 16] dx
= ∫ [0,π/3] √[(1 + 15cos^2(x))] dx
= ∫ [0,π/3] √15cos^2(x) + 1 dx
Using the substitution u = cos(x), we get:
L = ∫ [0,1] √(15u^2 + 1) du
This can be solved using trigonometric substitution, but the details are beyond the scope of this answer. The final result is:
L = 4/3 * √(15) * sinh^(-1)(√15/4) - √15/2
Therefore, the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3 is approximately 3.195 units.
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please describe how to troubleshoot if a LP model is
unbounded
If the LP model is unbounded, it means that there is no optimal solution for the problem. Here are the steps to troubleshoot an unbounded LP model:
Step 1: Check the constraints Firstly, ensure that the constraints are correct. Verify that the inequalities in the constraints are not of the same sign, such as all less than or all greater than. An incorrect inequality sign can cause an unbounded problem.Step 2: Check the objective function. Next, verify the objective function. Ensure that the function is either maximizing or minimizing the objective. If it's the wrong way around, this can cause the problem to be unbounded.Step 3: Check the feasibilityIf the LP model is unbounded, it means that the constraints are feasible, but the objective function is not bounded. You can check the feasibility of the model by using an initial feasible solution to test the objective function's value. If the value of the objective function is finite, it means that the problem is feasible. If it's not, the problem is infeasible.Step 4: Add constraints or change the objective function. If none of the above steps provide a solution, consider adding constraints or modifying the objective function to restrict the variables and bound the problem. If necessary, you may also consider changing the formulation of the problem to make it bounded.The objective is to make the LP problem bounded and to obtain an optimal solution within the given constraints. A feasible region can be transformed into a bounded feasible region, resulting in a bounded problem. Finally, the best approach to avoid an unbounded LP model is to verify the feasibility and the optimality of the problem before starting the simplex method.
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what is the solution of 10(w+3)=70
Answer: w = 4
Step-by-step explanation:
To solve the equation 10(w+3) = 70, we will work to get w by itself:
1. Divide by 10. This will get us closer to w.
(10( w + 3))/10 = 70/10
w + 3 = 7
2. We now have the equation w + 3 = 7. All we need to do now to get w by itself (or isolate it) is to subtract 3.
(w + 3) - 3 = 7 - 3
w = 7 - 3
w = 4
3. We can check our solution by inputting our found value, w = 4, into the equation.
10( 4 + 3 ) = 70
10(7) = 70
70=70
Because both sides of the equation are true, our solution of w = 4 is correct.
Answer: w = 4
Step-by-step explanation:
10(w+3)=70
10w + 30 = 70
10w = 40
w = 4
Compute the following: (Use C for the constant of integration) ∫1/ (x ^2−6x+14) dx=
The integral ∫1/ (x^2−6x+14) dx= 1/5 ln|(x-3)(x-2)| + C. This can be evaluated using partial fractions. The integrand is a rational function, which means that it can be written as the ratio of two polynomials.
The denominator of the rational function can be factored as (x-3)(x-2), so we can use partial fractions to decompose the integrand into two fractions: ∫1/ (x^2−6x+14) dx = ∫ (A/(x-3) + B/(x-2)) dx
where A and B are constants.
To find the values of A and B, we can multiply both sides of the equation by (x-3)(x-2), and then we can simplify the resulting equation. This gives us the following equations:
A + B = 1A - B = -1Solving these equations, we get A = 1/5 and B = -4/5.
Therefore, the integral ∫1/ (x^2−6x+14) dx= ∫ (1/5(x-3) - 4/5(x-2)) dx = 1/5 ln|(x-3)(x-2)| + C.
The integrand is a rational function, which means that it can be written as the ratio of two polynomials. The denominator of the rational function can be factored as (x-3)(x-2),
so we can use partial fractions to decompose the integrand into two fractions: ∫1/ (x^2−6x+14) dx = ∫ (A/(x-3) + B/(x-2)) dx
To find the values of A and B, we can multiply both sides of the equation by (x-3)(x-2), and then we can simplify the resulting equation. This gives us the following equations:
A + B = 1
A - B = -1
Solving these equations, we get A = 1/5 and B = -4/5.
Therefore, the integral ∫1/ (x^2−6x+14) dx= ∫ (1/5(x-3) - 4/5(x-2)) dx = 1/5 ln|(x-3)(x-2)| + C.
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True or false: a local variable is a variable defined inside a function that can only be used inside its function
Given statement 'a local variable is a variable defined inside a function that can only be used inside its function' is False
A local variable is a type of variable that we declare inside a block or a function, unlike the global variable. They can be used only by the statements that are inside the function or the block of the code. Local variables are not known to functions outside their own.
The variable declared is local within that function that is the declared variable is accessible inside that block itself, it cannot be accessible outside the given function.
Consider the following multiplication function:
ex - void multi()
{
int a = 10, b = 2, c ;
c = a * b ;
cout << c ;
}
int main()
{
cout << "value for c is :"<< c ;
return 0;
}
Here inside the multi function variable a, b, c are declared and initialized inside the function.
Thus, a local variable is defined inside the body of the function and is not accessible outside of the function.
Therefore, given statement 'a local variable is a variable defined inside a function that can only be used inside its function' is False
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The area model at the right shows a right triangle with side lengths a, b, and c such that a^2 + b^2 = c^2.
If the side lengths a increases by a small amount, but the lengths a increases by a small amount, but the lengths b and c do not change, which of the following statements will be true?
Select all that apply.
The statements that are true in the right triangle are
a² + b² > c² andm∠ACB = 90°What is a right angled triangle?A right angled triangle is a triangle in which one of its angles is 90°.
How to show which statements are true for the right triangle?Since the area model at the right shows a right triangle with side lengths a, b, and c such that a² + b² = c².
If the side lengths a increases by a small amount, but the lengths a increases by a small amount, but the lengths b and c do not change, we need to show which of the following statements will be true.
Now, if the side a increases by a small amount Δa, we have that
a + Δa > a
Squarring both sides, we have that
(a + Δa)² > a²
Adding b² to both sides, we have that
(a + Δa)² + b² > a² + b²
(a + Δa)² + b² > c² since a² + b² = c²
So, a² + b² > c² where a is the new value of a = a + Δa
Also, since a is perpendicular to b, we have that angle m∠ACB = 90°. Increasing a by a small amount Δa does not change a from being perpendicular to b, so we still have that m∠ACB = 90°.
So, the statements that are true in the right triangle are
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The scatter plot shows the relationship between pages read per week and age. What is the range of the cluster shown in the scatter plot?
A) 8 to 10 years of age
B) 8 to 17 years of age
C) 32 to 39 pages read per week
D) 32 to 72 pages read per week
part 2:
The scatter plot shows the relationship between pages read per week and age. What is the domain of the cluster shown in the scatter plot?
A) 8 to 10 years of age
B) 8 to 17 years of age
C) 32 to 39 pages read per week
D) 32 to 72 pages read per week
Answer:
part 1 of the question is d ,and part 2 of the question is b.
The range of the cluster shown in the scatter plot is 32 to 72 pages read per week.
Option D is the correct answer.
The domain of the cluster shown in the scatter plot is 8 to 17 years.
Option B is the correct answer.
What is a scatterplot?A scatterplot is a type of graphical display that is used to represent the relationship between two continuous variables.
In a scatterplot, each point represents the values of the two variables, with one variable being plotted along the x-axis and the other variable being plotted along the y-axis.
The position of each point on the graph represents the values of both variables for that particular observation.
We have,
The range in the scatterplot is the number of pages read per week.
Now,
The plot in the scatter plot is between 32 to 72 pages.
So,
The range of the cluster shown in the scatter plot is 32 to 72 pages read per week.
And,
The domain in the scatterplot is the number of ages in years.
Now,
The plot in the scatter plot is between 8 to 17 years.
So,
The domain of the cluster shown in the scatter plot is 8 to 17 years.
Thus,
The range of the cluster shown in the scatter plot is 32 to 72 pages read per week.
The domain of the cluster shown in the scatter plot is 8 to 17 years.
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Rotate point C(6,-3) 90 clockwise
PLEASE HELP
The answer is (-3, -6)
Step-by-step explanation:
turn the x into a y, and the y into a opposite x.
Write a method that takes a regularpolygon as a parameter, and changes the number of sides so it becomes an equilateral triangle (i. E. Set the number of sides to 3).
Answer: public static void randomize(RegularPolygon r){
int side = (int)((20-10) * Math.random()) + 10;
int length = (int)((12-5) * Math.random()) + 5;
// assuming the regularpolygon class has setSide and setLength methods.
r.set.Side(side);
r.setLength(length);
The randomize method is used to access and change the state of the RegularPolygon class attributes sides and length. The method accepts the class as an argument and assigns a random number of sides and length to the polygon object.
Step-by-step explanation:
11. Identify the properties below.
a. 5 + 6 = 6 + 5
b. 7 + (3 + 9) = (7 + 9) + 3
An animal shelter has 21 puppies if the puppies are 28% of the total dog and cat population how many dogs and cats are there in the animal shelter A.59
B.70
C.49
D.75
Find the area of hexagon DEFGHI.
Step-by-step explanation:
Break it up into two trapezoids as shown
area = trap1 + trap2
= 2 * (7+3) / 2 + 3 * ( 7 + 3) / 2 = 10 + 15 = 25 units^2
Which is the graph of y = [x]-2?
PLEASE HELP TIMED PLEASE
Answer:
3rd graph
Step-by-step explanation:
please help will mark brainliest!!!!!!!!
Refer to the figure at the right.
Suppose angle 5 = 147º. Find angle 1
Answer:
37
Step-by-step explanation:
147= 15x +5+ 22x +4. 120 = 37
Answer:
If angle 5=147 then angle 2 would be 33 since it needs to equal 180
then angle one would also equal angle 2, or =33
Step-by-step explanation:
Two angles are supplementary. One measures 7x - 9 and the other measures 4x + 3. Find x and the measure of the smaller angle
Answer:
Supplementary angles add up to 180°
180=7x-9+4x+3
180=7x+4x-9+3
180=11x-7
180+7=11x
187=11x
11x=187
x=187/11
x=17
Therefore x = 17
Which statement correctly compares the function shown on this graph with the function y= 6x - 1? y 10 8 6 4 2 -10 8 6 4 2 -2 2 4 6 8 10 2 6
A. The function shown on the graph has a greater rate of change and a higher starting point. A
B. The function shown on the graph has a smaller rate of change and a lower starting point.
C. The function shown on the graph has a smaller rate of change, but a higher starting point.
D. The function shown on the graph has a greater rate of change and a lower starting point.
Answer:
B. The function shown on the graph has a smaller rate of change and a lower starting point.
Step-by-step explanation:
✍️The function y = 6x - 1, has:
slope (m) = 6, and
Starting point/y-intercept (b) = -1
✍️Let's find the slope (m) and the starting point (y-intercept) of the function shown on the graph:
Using the points, (0, -6) and (2, 4),
Slope = \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 -(-6)}{2 - 0} = \frac{10}{2} = 5 \)
Slope (m) = 5
The strating value is the value of y when x = 0. In order words, it is the point at which the line of the function intercepts the y-axis.
The y-axis is intercepted at y = -6.
Therefore, the starting value (b) = -6.
Therefore, the statement correctly compares the function shown on the graph above with the function y = 6x - 1 is:
B. The function shown on the graph has a smaller rate of change and a lower starting point.
Comparing their slopes, 5 is smaller than 6.
Comparing their starting points, -6 is lower than -1.
Answer:
B
Step-by-step explanation:
Correct on a p e x
Multiply the number by 4. Add 10 to the product. Divide this sum by 2. Subtract 5 from the quotient.
The first number is 1 and the result is 2
The second number is 5 and the result is 10
the third number is 9 and the result is 18
the fourth number is 10 and the result is 20
Write a conjecture that relates the result of the process to the original number selected. part a)
Represent the original number as n.
Answer is 2n
part b Represent the original number as n, and use deductive reasoning to prove the conjecture in part (a). Multiply the number by 4.
Help with part b please.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following instructions :
It can be deduced from part a that the final result will be twice the original number 'n'
The number 'n' multiplied by 4 = (4 * n) = 4n
10 added to 4n = 4n + 10
The result of the sum divide by 2 = (4n + 10) / 2
= 2n + 5
5 subtracted from the result of the quotient obtained : 2n +5 - 5 = 2n
Where n is the original number.
2n = twice the original number.
please help me thank you
Answer:
A
Step-by-step explanation:
It's Point A
2.2. South African friends of the Netherlands couple departed from Pretoria at 04h30am to spend the holiday with them. Their journey is described as follows: On their way from Polokwane they took the turn-off to the R521 route. Rest for 45 minutes at Dendron and took 15 minutes to do someshopping and till up the car's fuel tank at All days. 2.2.1. If the scale of the map is given as 1: 3 000 000 and the distance measured on the map between Beitbridge and Musina is 1,3 cm. calculate (in km) the actual distance between Beitbridge and Musina. ● (3)
The actual distance between Beitbridge and Musina is 3,900,000 kilometers.
To calculate the actual distance between Beitbridge and Musina, given the scale of the map and the measured distance on the map, we can use the concept of scale.
The scale of the map is given as 1:3,000,000, which means that 1 cm on the map represents 3,000,000 cm in real life.
The measured distance on the map between Beitbridge and Musina is 1.3 cm.
To find the actual distance, we can set up a proportion using the scale:
1 cm on the map / 3,000,000 cm in real life = 1.3 cm on the map / x km in real life.
Simplifying the proportion, we have:
1 / 3,000,000 = 1.3 / x.
Cross-multiplying, we get:
x = (1.3 * 3,000,000) / 1.
x = 3,900,000 / 1.
x = 3,900,000 km.
The actual distance between Beitbridge and Musina is 3,900,000 kilometers.
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a smartphone was purposefully dropped from a height of 10 meters to test its durability from external physical impact. it will be damaged 100% of the time, but the damage can occur in different parts of the phone. it has been shown that 76% of the damages occur in the glass screen, while the other 24% occur in the battery. a number of smartphones were tested and the tests were independent. find the probability that the first time you observe a battery damage is during the third trial or later.
Answer:
what the quistion?
Step-by-step explanation:
sry i cant spell
The probability that the first time a battery damage is observed is during the third trial or later is 42.74%.
To solve this problem, we can use the geometric distribution, which models the number of trials until the first success in a sequence of independent trials. In this case, the probability of success is 0.24 (the probability of a battery damage) and the probability of failure is 0.76 (the probability of a glass screen damage).
The probability of observing a battery damage for the first time on the third trial or later can be calculated as the complement of the probability of observing a battery damage on the first or second trial.
The probability of observing a battery damage on the first trial is 0.24, and the probability of observing a battery damage on the second trial is (0.76)(0.24) = 0.1824 (the probability of no battery damage on the first trial times the probability of battery damage on the second trial). Therefore, the probability of observing a battery damage for the first time on the third trial or later is 1 - 0.24 - 0.1824 = 0.5776.
However, the question asks for the probability of observing a battery damage for the first time on the third trial or later, which means we need to take into account the fact that we may have observed a battery damage before the third trial. Therefore, we need to adjust our calculation by subtracting the probability of observing a battery damage for the first time on the first or second trial from our previous result.
The probability of observing a battery damage for the first time on the first or second trial is 0.24 + 0.1824 = 0.4224. Therefore, the probability of observing a battery damage for the first time on the third trial or later is 0.5776 - 0.4224 = 0.1552 or 15.52%.
Therefore, the probability that the first time a battery damage is observed is during the third trial or later is 42.74%
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how to graph a line with a slope of 2 and (0,-8) y-intercept
Answer:
If i am understanding your question correctly the slope equation would be y=2x+(-8)
Step-by-step explanation:
So 2 is gonna be your slope -8 is your y intercept, you are going to put a point at (0,-8) and the slope is always rise over run so you are going to rise up 2 points on your y axis and move to the right 1 unit on your x axis. You should have two points now, to finish your line keep going up 2 units and to the right 1 unit.
Hope this helps!