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High School Math : Lines

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Example Questions

Example Question #4 : How To Find The Slope Of A Perpendicular Line

Find the slope of the line perpendicular to $y + \frac{2}{3}x = 12$ .

Possible Answers:

$-\frac{2}{3}$

$-\frac{3}{2}$

$\frac{2}{3}$

$-\frac{1}{12}$

$\frac{3}{2}$

Correct answer:

$\frac{3}{2}$

Explanation:

Put this equation into slope-intercept form, y = mx + b, to find the slope, m.

Do this by subtracting $\frac{2}{3}x$ from both sides of the equation:

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

The slope of this line is $-\frac{2}{3}$ .

The slope of the perpendicular line is the negative reciprocal. Switch the numerator and denominator, and then multiply by :

$-\frac{2}{3} \Rightarrow -\frac{3}{2} \Rightarrow -\frac{3}{2} \times -1 \Rightarrow \frac{3}{2}$

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Example Question #1 : How To Find The Slope Of A Perpendicular Line

What is the slope of the line perpendicular to $y=\frac{2}{3}x+\frac{1}{2}$ ?

Possible Answers:

$-\frac{3}{2}$

$-\frac{2}{3}$

$\frac{1}{3}$

$\frac{3}{2}$

$\frac{2}{3}$

Correct answer:

$-\frac{3}{2}$

Explanation:

In standard y=mx+b form, is the slope.

The slope of a perpendicular line is the negative reciprocal of the original line.

For our given line, the slope is $\frac{2}{3}$ . Therefore, the slope of the perpendicular line is $-\frac{3}{2}$ .

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Example Question #1 : How To Find The Slope Of A Perpendicular Line

Find the slope of this line: 2x-8y=16.

Possible Answers:

m=4

$m=-\frac{1}{4}$

m=-4

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

$m=\frac{3}{4}$

Correct answer:

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

Explanation:

Isolate for so that the equation now reads

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

The slope is $\frac{1}{4}$ .

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Example Question #41 : Coordinate Geometry

Which of the following are perpendicular to the line with the formula $y = -\frac{1}{3}X + 3$ ?

I. y = 3X

II. $y = \frac{1}{3}X + 3$

III. $y = \frac{4.5}{1.5}X -3$

Possible Answers:

I and III

III

II and III

Correct answer:

I and III

Explanation:

The slope of a perpendicular line is equal to the negative reciprocal of the original line. This means that the slope of our perpendicular line must be 3. We can also note that $\frac{4.5}{1.5}$ is also equal to 3, so both of these slopes are correct. The y-intercept does not matter, as the slope is the only thing that determines the slant of the line. Therefore, numerals I and III are both correct.

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Example Question #42 : Coordinate Geometry

Which of the following lines is perpendicular to y=2x+9 ?

Possible Answers:

y=2x-7

$y=-\frac{1}{2}x-12$

y=-2x-5

$y=\frac{1}{2}x-11$

$y=\frac{1}{2}x+11$

Correct answer:

$y=-\frac{1}{2}x-12$

Explanation:

In order for two lines to be perpendicular to each other, their slopes must be opposites and reciprocals of each other, meaning the fraction must be flipped upside down and the signs must be changed. In this situation, the original equation had a slope of , so the perpendicular slope must be $-\frac{1}{2}$ .

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Example Question #43 : Coordinate Geometry

Which of the following lines will be perpendicular to y=2x+5 ?

Possible Answers:

y=x+5

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

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

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

y=-2x-2

Correct answer:

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

Explanation:

Two lines are perpendicular if they have opposite reciprocal slopes. When a line is in standard y=mx+b form, the is the slope. A perpendicular line will have a slope of $-\frac{1}{m}$ .

The slope of our given line is . Therefore we want a slope of $-\frac{1}{2}$ . The only line with the correct slope is $y=-\frac{1}{2}x+1$ .

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Example Question #41 : Lines

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

Possible Answers:

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

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

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

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

y=x

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 #42 : Lines

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

Possible Answers:

y = -5x + 7

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

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

y = 7x + 2

y = 5x - 10

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 #3 : Parallel Lines

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

Possible Answers:

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

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

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

y=-x

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

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 #43 : Lines

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

Possible Answers:

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

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

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

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

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

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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High School Math : Lines

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #4 : How To Find The Slope Of A Perpendicular Line

Example Question #1 : How To Find The Slope Of A Perpendicular Line

Example Question #1 : How To Find The Slope Of A Perpendicular Line

Example Question #41 : Coordinate Geometry

Example Question #42 : Coordinate Geometry

Example Question #43 : Coordinate Geometry

Example Question #41 : Lines

Example Question #42 : Lines

Example Question #3 : Parallel Lines

Example Question #43 : Lines

All High School Math Resources

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