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PSAT Math : How to find the equation of a parallel line

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Example Questions

Example Question #1 : Coordinate Geometry

Which of the following is the equation of a line that is parallel to the line 4x – y = 22 and passes through the origin?

Possible Answers:

4x – y = 0

4x = 8y

(1/4)x + y = 0

4x + 8y = 0

y – 4x = 22

Correct answer:

4x – y = 0

Explanation:

We start by rearranging the equation into the form y = mx + b (where m is the slope and b is the y intercept); y = 4x – 22
Now we know the slope is 4 and so the equation we are looking for must have the m = 4 because the lines are parallel. We are also told that the equation must pass through the origin; this means that b = 0.

In 4x – y = 0 we can rearrange to get y = 4x. This fulfills both requirements.

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Example Question #1 : Coordinate Geometry

What line is parallel to 2x + 5y = 6 through (5, 3)?

Possible Answers:

y = 3/5x – 2

y = 5/2x + 3

y = 5/3x – 5

y = –2/5x + 5

y = –2/3x + 3

Correct answer:

y = –2/5x + 5

Explanation:

The given equation is in standard form and needs to be converted to slope-intercept form which gives y = –2/5x + 6/5. The parallel line will have a slope of –2/5 (the same slope as the old line). The slope and the given point are substituted back into the slope-intercept form to yield y = –2/5x +5.

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Example Question #3 : Coordinate Geometry

What line is parallel to y=2x-1 through (1,-3) ?

Possible Answers:

-2x+y=-5

x+3y=11

x-2y=6

3x+2y=-4

2x-y=7

Correct answer:

-2x+y=-5

Explanation:

The slope of the given line is m=2 and a parallel line would have the same slope, so we need to find a line through (1,-3) with a slope of 2 by using the slope-intercept form of the equation for a line. The resulting line is y=2x-5 which needs to be converted to the standard form to get -2x+y=-5 .

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Example Question #114 : Psat Mathematics

Find the equation of a line parallel to $\small y = 2x - 3$ that also passes through the point $\small \left ( 3 , 2\right )$ .

Possible Answers:

$\small y = 2x - 4$

$\small \small y = 2x + 4$

$\small \small y = 3x + 4$

$\small y = 2x + 3$

$\small y = 3x - 4$

Correct answer:

$\small y = 2x - 4$

Explanation:

Since they are parallel, the line will have the same slope as $\small \small y = 2x - 3$ .

Thus, it will take the form $\small \small y = 2x + b$ .

We then use the point (3,2) to solve for $\small b$ :

$\small \left ( 2\right ) = 2\left ( 3\right ) + b$

$\small 2 = 6 + b$

$\small - 4 = b$

so the equation of the line is

$\small y = 2x - 4$

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

In the -plane, the line y=ax-3 is parallel to the line 3y-6x=12 . What is the value of ?

Possible Answers:

Correct answer:

Explanation:

In this equation, is equal to the slope of the line. You have been given a line parallel to the line containing variable , and since parallel lines have the same slope, all you need to do is figure out the slope of 3y-6x=12 in order to figure out what is. To figure out the slope of , you need to convert the equation into y=mx+b form, which means isolating on one side of the equation.

3y - 6x = 12

3y = 12 + 6x

y = 4 + 2x = 2x+4

Given this solution, the slope of the parallel lines, and thus , is equal to 2.

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

Which of the following lines has zero points of intersection with the line, 3x-2y=12 ?

Possible Answers:

$y=\frac{3}{2}x -6$

$y=\frac{3}{2}x -10$

$y=-\frac{3}{2}x -5$

$y=-\frac{2}{3}x -6$

$y=-\frac{2}{3}x -4$

Correct answer:

$y=\frac{3}{2}x -10$

Explanation:

This prompt asks you to find a line that is parallel to the one given. Parallel lines have no points of intersection (as opposed to intersecting lines which have 1 point of intersection). Parallel lines have the same slope, but different y-intercepts. If they had the same y-intercept, then they would actually be the same line.

We can find the slope of the first line by converting it to slope-intercept form.

3x-2y=12

First, subtract 3x from both sides.

-2y=-3x +12

Then, divide both sides by -2.

$y=\frac{3}{2}x -6$

The slope of the line is 3/2. The only answer that has that same slope, but a different y-intercept is $y=\frac{3}{2}x -10$ .

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PSAT Math : How to find the equation of a parallel line

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1 : Coordinate Geometry

Example Question #1 : Coordinate Geometry

Example Question #3 : Coordinate Geometry

Example Question #114 : Psat Mathematics

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

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

All PSAT Math Resources

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