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High School Math : How to find out if lines are parallel

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Example Questions

Example Question #1 : Parallel Lines

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

Possible Answers:

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

y=x

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

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

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

Correct answer:

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

Explanation:

Lines are parallel if they have the same slope. In standard y=mx+b 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.

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Example Question #46 : Coordinate Geometry

Which of the following lines is parallel to y = 5x + 3 ?

Possible Answers:

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

y = 5x - 10

y = 7x + 2

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

y = -5x + 7

Correct answer:

y = 5x - 10

Explanation:

Two lines that are parallel have the same slope. The slope of y = 5x + 3 is , so we want another line with a slope of . The only other line with a slope of is y = 5x - 10 .

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Example Question #2 : Parallel Lines

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

Possible Answers:

y=-x

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

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

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

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

Correct answer:

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

Explanation:

Lines are parallel if they have the same slope. In standard y=mx+b 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.

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Example Question #48 : Coordinate Geometry

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

Two lines are parallel if they have the same slope. When a line is in standard y=mx+b 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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Example Question #3 : Parallel Lines

Are the following lines parallel?

y = 2x - 5

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

Possible Answers:

It cannot be determined from the information given

Yes

Correct answer:

Explanation:

By definition, two lines are parallel if they have the same slope. Notice that since we are given the lines in the y = mx + b 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.

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Example Question #52 : Coordinate Geometry

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

Possible Answers:

y=-4x- 3

y=x

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

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

y=-x

Correct answer:

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

Explanation:

Parallel lines have the same slope. In slope-intercept form, y=mx+b , 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 y=mx+b form, the equation becomes $y =0x+\frac{1}{4}$ . Therefore the slope is actually , not $\frac{1}{4}$ .

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High School Math : How to find out if lines are parallel

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Parallel Lines

Example Question #46 : Coordinate Geometry

Example Question #2 : Parallel Lines

Example Question #48 : Coordinate Geometry

Example Question #3 : Parallel Lines

Example Question #52 : Coordinate Geometry

All High School Math Resources

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