SSAT Upper Level Quantitative - How to find out if lines are parallel

Which of the following lines is parallel with the line $y=-\frac{1}{5}x+1$ ?

$y=-\frac{1}{5}x+9$

$y=\frac{1}{5}x-2$

Explanation

Parallel lines have the same slope. The slope of a line in slope-intercept form is the value of . So, the slope of the line $y=-\frac{1}{5}x+1$ is $-\frac{1}{5}$ . That means that for the two lines to be parallel, the slope of the second line must also be $-\frac{1}{5}$ .

Which of the following lines is parallel to the line ?

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

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

Explanation

For two lines to be parallel, their slopes must be the same. Thus, the line that is parallel to the given one must also have a slope of .

Which of the following lines is parallel to the line ?

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

$y=-\frac{1}{2}x+19$

Explanation

Parallel lines have the same slope. The slope of a line in slope-intercept form is the value of . So, the slope of the line is . That means that for the two lines to be parallel, the slope of the second line must also be .

Which of the following lines is parallel with the line with equation ?

Explanation

Which of the following lines is parallel to the line ?

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

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

Explanation

Which of the following lines is parallel to the line ?

$y=\frac{1}{6}x-9$

$y=-\frac{1}{6}x+19$

Explanation

Lines that are parallel have the same slope, so the correct answer must also have the slope of .

Which of the following lines is parallel with the line $-4x+\frac{1}{2}y=8$ ?

Explanation

First, put the given equation in the more familiar format to find out the slope of the given line.

$-4x+\frac{1}{2}y=8$

$\frac{1}{2}y=4x+8$

Lines that are parallel must share the same slope. Thus, the line that is parallel has a slope of .

Which of the following lines is parallel to the line with the equation $y=\frac{1}{4}x+3$ ?

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

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

Explanation

Parallel lines have the same slope. The slope of a line in slope-intercept form is the value of . So, the slope of the line $y=\frac{1}{4}x+3$ is $\frac{1}{4}$ . That means that for the two lines to be parallel, the slope of the second line must also be $\frac{1}{4}$ .