How to find the equation of a parallel line

SSAT Upper Level Quantitative · Learn by Concept

Help Questions

SSAT Upper Level Quantitative › How to find the equation of a parallel line

1 - 10

Find the equation of a line that goes through the point and is parallel to the line with the equation .

CORRECT

$y=\frac{1}{4}x-4$

Explanation

For lines to be parallel, they must have the same slope. The slope of the line we are looking for then must be .

The point that's given in the equation is also the y-intercept.

Using these two pieces of information, we know that the equation for the line must be

There is a line defined by the equation below:

There is a second line that passes through the point and is parallel to the line given above. What is the equation of this second line?

$y=-\frac{3}{4}x+2.75$

CORRECT

$y=-\frac{3}{4}x+1.25$

$y=\frac{3}{4}x+2.75$

$y=\frac{3}{4}x+1.25$

$y=\frac{3}{4}x+2.625$

Explanation

Parallel lines have the same slope. Solve for the slope in the first line by converting the equation to slope-intercept form.

3x + 4y = 12

4y = _–_3x + 12

y = –(3/4)x + 3

slope = _–_3/4

We know that the second line will also have a slope of _–_3/4, and we are given the point (1,2). We can set up an equation in slope-intercept form and use these values to solve for the y-intercept.

y = mx + b

2 = _–_3/4(1) + b

2 = _–_3/4 + b

b = 2 + 3/4 = 2.75

Plug the y-intercept back into the equation to get our final answer.

y = –(3/4)x + 2.75

Find the equation of the line that goes through the point and is parallel to the line with the equation .

CORRECT

$y=-\frac{1}{2}x+7$

Explanation

Because the two lines are parallel, we know that the slope of the line we need to find must also be .

We can then plug in the given point and the slope into the equation of a line to find the y-intercept.

Now, we can write the equation of the line.

Find the equation of the line that passes through the point and is parallel to the line with the equation $y=\frac{3}{2}x-1$ .

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

CORRECT

$y=\frac{3}{2}x+\frac{7}{2}$

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

$y=\frac{3}{2}x-\frac{1}{2}$

Explanation

Because the two lines are parallel, we know that the slope of the line we need to find must also be $\frac{3}{2}$ .

Now, we can plug in the point given by the question to find the y-intercept.

$-2=\frac{3}{2}(1)+b$

$b+\frac{3}{2}=-2$

$b=-\frac{7}{2}$

From this, we can write the following equation:

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

Find the equation of the line that passes through the point and is parallel to the line with the equation .

CORRECT

$y=\frac{1}{3}x+2$

$y=-\frac{1}{3}x+2$

Explanation

Because the two lines are parallel, we know that the slope of the line we need to find must also be .

Next, plug in the point given by the question to find the y-intercept of the line.

Now, we know that the equation of the line must be .

Find the equation of the line that passes through the point and is parallel to the line with the equation .

CORRECT

$y=\frac{1}{2}x+4$

Explanation

Because the two lines are parallel, we know that the slope of the line we need to find must also be .

Next, plug in the point given by the question to find the y-intercept of the line.

Now, we know the equation of the line must be .

Find the equation of the line that passes through the point and is parallel to the line with the equation .

CORRECT

Explanation

Because the two lines are parallel, we know that the slope of the line we need to find must also be .

Next, plug in the point given by the question to find the y-intercept of the line.

Now, we can write the equation for the line:

What line is parallel to , and passes through the point ?

$y = \frac{-5}{3}x + 6$

CORRECT

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

$y = \frac{1}{3}x - 3$

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

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

Explanation

Converting the given line to slope-intercept form we get the following equation:

$y = \frac{-5}{3}x + \frac{8}{3}$

For parallel lines, the slopes must be equal, so the slope of the new line must also be $\frac{-5}{3}$ . We can plug the new slope and the given point into the slope-intercept form to solve for the y-intercept of the new line.

$-4 = \frac{-5}{3}(6) + b$

Use the y-intercept in the slope-intercept equation to find the final answer.

$y = \frac{-5}{3}x + 6$

Find the equation of the line that passes through the point and is parallel to the line with the equation $y=\frac{1}{2}x-2$ .

$y=\frac{1}{2}x+4$

CORRECT

$y=\frac{1}{2}x-2$

Explanation

Because the two lines are parallel, we know that the slope of the line we need to find must also be $\frac{1}{2}$ .

Next, plug in the point given by the question to find the y-intercept of the line.

$3=\frac{1}{2}(-2)+b$

Now, we knwo the equation of the line must be $y=\frac{1}{2}x+4$ .

What line is parallel to at ?

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

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

CORRECT

$y=-\frac{3}{2}x+8$

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

None of the answers are correct

Explanation

Find the slope of the given line: (slope intercept form)

$y=\frac{-2}{3}x+2$ therefore the slope is $\frac{-2}{3}$

Parallel lines have the same slope, so now we need to find the equation of a line with slope $\frac{-2}{3}$ and going through point by substituting values into the point-slope formula.