GRE Math : How to find the equation of a line

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Example Question #1 : How To Find The Equation Of A Line

What is the equation of the straight line passing through (–2, 5) with an x-intercept of 3?

Possible Answers:

y = –x + 3

y = –x – 3

y = –5x – 3

y = –5x + 3

Correct answer:

y = –x + 3

Explanation:

First you must figure out what point has an x-intercept of 3. This means the line crosses the x-axis at 3 and has no rise or fall on the y-axis which is equivalent to (3, 0). Now you use the formula (y₂–y₁)/(x₂– x₁) to determine the slope of the line which is (5 – 0)/(–2 – 3) or –1. Now substitute a point known on the line (such as (–2, 5) or (3, 0)) to determine the y-intercept of the equation y = –x + b. b = 3 so the entire equation is y = –x + 3.

Gre_quant_179_01

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Example Question #2 : How To Find The Equation Of A Line

What is the equation of the line passing through (–1,5) and the upper-right corner of a square with a center at the origin and a perimeter of 22?

Possible Answers:

y = (–3/5)x + 22/5

y = (3/5)x + 22/5

y = –x + 5

y = (–3/5)x + 28/5

y = (–1/5)x + 2.75

Correct answer:

y = (–3/5)x + 22/5

Explanation:

If the square has a perimeter of 22, each side is 22/4 or 5.5. This means that the upper-right corner is (2.75, 2.75)—remember that each side will be "split in half" by the x and y axes.

Using the two points we have, we can ascertain our line's equation by using the point-slope formula. Let us first get our slope:

m = rise/run = (2.75 – 5)/(2.75 + 1) = –2.25/3.75 = –(9/4)/(15/4) = –9/15 = –3/5.

The point-slope form is: y – y₀ = m(x – x₀). Based on our data this is: y – 5 = (–3/5)(x + 1); Simplifying, we get: y = (–3/5)x – (3/5) + 5; y = (–3/5)x + 22/5

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Example Question #1 : How To Find The Equation Of A Line

What is the equation of a line passing through the points (-2,17) and (5,-11) ?

Possible Answers:

y=-4x+9

$y=\frac{14}{3}x+17$

y=4x+17

y=-27x-15

$y=\frac{12}{5}x-20$

Correct answer:

y=-4x+9

Explanation:

Based on the information provided, you can find the slope of this line easily. From that, you can use the point-slope form of the equation of a line to compute the line's full equation. The slope is merely:

$\frac{rise}{run}=\frac{17-(-11)}{-2-5}=\frac{17+11}{-7}=\frac{-28}{7}=-4$

Now, for a point (a,b) and a slope , the point-slope form of a line is:

y-b=m(x-a)

Let's use (-2,17) for our point (a,b)

This gives us:

y-17=-4(x+2)

Now, distribute and solve for :

y-17=-4x-8

y=-4x+9

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Example Question #4 : How To Find The Equation Of A Line

What is the equation of a line passing through the two points (41,11) and (4,-9) ?

Possible Answers:

y=14x-18

$y=\frac{17}{14}x-\frac{148}{25}$

$y=\frac{20}{37}x-\frac{413}{37}$

$y=\frac{20}{27}x-\frac{14}{15}$

$y=\frac{7}{2}x-\frac{85}{3}$

Correct answer:

$y=\frac{20}{37}x-\frac{413}{37}$

Explanation:

$\frac{rise}{run}=\frac{11-(-9)}{41-4}=\frac{11+9}{37}=\frac{20}{37}$

Now, for a point (a,b) and a slope , the point-slope form of a line is:

y-b=m(x-a)

Let's use (4,-9) for our point (a,b)

This gives us:

$y+9=\frac{20}{37}(x-4)$

Now, distribute and solve for :

$y+9=\frac{20}{37}x-\frac{80}{37}$

$y=\frac{20}{37}x-\frac{80}{37}-9$

$y=\frac{20}{37}x-\frac{80}{37}-\frac{333}{37}$

$y=\frac{20}{37}x-\frac{413}{37}$

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Example Question #5 : How To Find The Equation Of A Line

What is the equation of a line passing through (4,-12) with a -intercept of ?

Possible Answers:

$y=\frac{-15}{4}x+12$

y=-22x+15

$y=\frac{-21}{4}x+9$

$y=\frac{27}{5}x+9$

y=-5x-9

Correct answer:

$y=\frac{-21}{4}x+9$

Explanation:

Based on the information that you have been provided, you can quickly find the slope of your line. Since the y-intercept is , you know that the line contains the point (0,9) . Therefore, the slope of the line is found:

$\frac{-12-9}{4-0}=\frac{-21}{4}$

Based on this information, you can use the standard slope-intercept form to find your equation:

y=mx+b , where $m=\frac{-21}{4}$ and b=9

$y=\frac{-21}{4}x+9$

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Example Question #1 : How To Find The Equation Of A Line

Given the graph of the line below, find the equation of the line.

Act_math_160_04

Possible Answers:

y=x-4

$y=\frac{10}{3}x-4$

y=-5x-4

y=-x

Correct answer:

$y=\frac{10}{3}x-4$

Explanation:

To solve this question, you could use two points such as (1.2,0) and (0,-4) to calculate the slope which is 10/3 and then read the y-intercept off the graph, which is -4.

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Example Question #241 : Geometry

Which line passes through the points (0, 6) and (4, 0)?

Possible Answers:

y = 1/5x + 3

y = 2/3x –6

y = –3/2 – 3

y = 2/3 + 5

y = –3/2x + 6

Correct answer:

y = –3/2x + 6

Explanation:

P₁ (0, 6) and P₂ (4, 0)

First, calculate the slope: m = rise ÷ run = (y₂ – y₁)/(x₂– x₁), so m = –3/2

Second, plug the slope and one point into the slope-intercept formula:

y = mx + b, so 0 = –3/2(4) + b and b = 6

Thus, y = –3/2x + 6

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Example Question #1 : Coordinate Geometry

What line goes through the points (1, 3) and (3, 6)?

Possible Answers:

–2x + 2y = 3

4x – 5y = 4

–3x + 2y = 3

2x – 3y = 5

3x + 5y = 2

Correct answer:

–3x + 2y = 3

Explanation:

If P₁(1, 3) and P₂(3, 6), then calculate the slope by m = rise/run = (y₂ – y₁)/(x₂ – x₁) = 3/2

Use the slope and one point to calculate the intercept using y = mx + b

Then convert the slope-intercept form into standard form.

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Example Question #144 : Coordinate Geometry

What is the slope-intercept form of $\dpi{100} \small 8x-2y-12=0$ ?

Possible Answers:

$\dpi{100} \small y=-2x+3$

$\dpi{100} \small y=4x-6$

$\dpi{100} \small y=-4x+6$

$\dpi{100} \small y=4x+6$

$\dpi{100} \small y=2x-3$

Correct answer:

$\dpi{100} \small y=4x-6$

Explanation:

The slope intercept form states that $\dpi{100} \small y=mx+b$ . In order to convert the equation to the slope intercept form, isolate $\dpi{100} \small y$ on the left side:

$\dpi{100} \small 8x-2y=12$

$\dpi{100} \small -2y=-8x+12$

$\dpi{100} \small y=4x-6$

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Example Question #61 : Coordinate Geometry

A line is defined by the following equation:

7x+28y=84

What is the slope of that line?

Possible Answers:

$-\frac{1}{4}$

$\frac{1}{4}$

Correct answer:

$-\frac{1}{4}$

Explanation:

The equation of a line is

y=mx + b where m is the slope

Rearrange the equation to match this:

7x + 28y = 84

28y = -7x + 84

y = -(7/28)x + 84/28

y = -(1/4)x + 3

m = -1/4

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GRE Math : How to find the equation of a line

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 : How To Find The Equation Of A Line

Example Question #2 : How To Find The Equation Of A Line

Example Question #1 : How To Find The Equation Of A Line

Example Question #4 : How To Find The Equation Of A Line

Example Question #5 : How To Find The Equation Of A Line

Example Question #1 : How To Find The Equation Of A Line

Example Question #241 : Geometry

Example Question #1 : Coordinate Geometry

Example Question #144 : Coordinate Geometry

Example Question #61 : Coordinate Geometry

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