How to find out if lines are parallel

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Math › How to find out if lines are parallel

Questions 1 - 6

1

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

$y= \frac {1}{4} x-20$

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

Explanation

Parallel lines have the same slope. In slope-intercept form, , is the slope.

$y=\frac{1}{4}x-3$

Here the slope is $\frac{1}{4}$ ; thus, any line that is parallel to the line in question will also have a slope of $\frac{1}{4}$ .

Only one answer choice satisfies this requirement: $y= \frac {1}{4} x-20$

Note: the answer choice $y= \frac {1}{4}$ is incorrect. If put into form, the equation becomes $y =0x+\frac{1}{4}$ . Therefore the slope is actually , not $\frac{1}{4}$ .

2

Are the following lines parallel?

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

No

Yes

It cannot be determined from the information given

Explanation

By definition, two lines are parallel if they have the same slope. Notice that since we are given the lines in the format, and our slope is given by , it is clear that the slopes are not the same in this case, and thus the lines are not parallel.

3

Which of the following lines is parallel to ?

$y = -\frac{1}{5}x + 6$

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

Explanation

Two lines that are parallel have the same slope. The slope of is , so we want another line with a slope of . The only other line with a slope of is .

4

Which of these lines is parallel to $y=\frac{2}{3}x+\frac{5}{6}$ ?

$y=\frac{2}{3}x-12$

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

$y=\frac{3}{2}x+\frac{5}{6}$

$y=-\frac{3}{2}x+\frac{5}{6}$

Explanation

Lines are parallel if they have the same slope. In standard form, is the slope.

For our given equation, the slope is $\frac{2}{3}$ . Only $y=\frac{2}{3}x-12$ has the same slope.

5

Which of these lines is parallel to $y=\frac{4}{7}x+\frac{1}{3}$ ?

$y=\frac{4}{7}x-1$

$y=\frac{7}{4}x+\frac{1}{3}$

$y=-\frac{4}{7}x+\frac{2}{3}$

$y=-\frac{7}{4}x^$

Explanation

Lines are parallel if they have the same slope. In standard form, is the slope.

For our given equation, the slope is $\frac{4}{7}$ . Only $y=\frac{4}{7}x-1$ has the same slope.

6

Which of the following lines will be parallel to $y=\frac{3}{4}x+12$ ?

$y=\frac{3}{4}x-5$

$y=-\frac{4}{3}x+12$

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

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

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

Explanation

Two lines are parallel if they have the same slope. When a line is in standard form, the is the slope.

For the given line $y=\frac{3}{4}x+12$ , the slope will be $\frac{3}{4}$ . Only one other line has a slope of $\frac{3}{4}$ : $y=\frac{3}{4}x-5$

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