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Algebra 1 : Equations of Lines

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Example Questions

Example Question #662 : Functions And Lines

Give the -intercept of the line of the equation

3x+2= 6y

Possible Answers:

$\left ( \frac{1}{3}, 0 \right )$

$\left ( 2, 0 \right )$

$\left ( -\frac{2}{3}, 0 \right )$

$\left ( -1\frac{1}{2}, 0 \right )$

$\left (3, 0 \right )$

Correct answer:

$\left ( -\frac{2}{3}, 0 \right )$

Explanation:

The -coordinate of the -intercept of a line can be found by substituting 0 for in its equation and solving for :

3x+2= 6y

$3x+2= 6 \cdot 0$

3x+2= 0

3x+2- 2 = 0- 2

3x = - 2

$3x \div 3 = - 2 \div 3$

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

The -intercept is the point $\left ( -\frac{2}{3}, 0 \right )$ .

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Example Question #663 : Functions And Lines

Give the -intercept of the line of the equation

7y+ 4x = 29

Possible Answers:

$\left ( \frac{7}{29}, 0 \right )$

$\left ( 4\frac{1}{7}, 0 \right )$

$\left (- \frac{4}{7}, 0 \right )$

$\left ( 7\frac{1}{4}, 0 \right )$

$\left ( \frac{4}{29}, 0 \right )$

Correct answer:

$\left ( 7\frac{1}{4}, 0 \right )$

Explanation:

The -coordinate of the -intercept of a line can be found by substituting 0 for in its equation and solving for :

7y+ 4x = 29

$7 \cdot 0 + 4x = 29$

0 + 4x = 29

4x = 29

$4x \div 4 = 29 \div 4$

$x = \frac{29}{4} = 7 \frac{1}{4}$

The -intercept is the point $\left ( 7\frac{1}{4}, 0 \right )$ .

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Example Question #23 : How To Find Out If A Point Is On A Line With An Equation

Give the -intercept of the line of the equation

8y = 3x + 7

Possible Answers:

$\left ( -2\frac{2}{3}, 0 \right )$

$\left ( -2\frac{1}{3}, 0 \right )$

$\left ( -\frac{3}{7}, 0 \right )$

$\left ( -\frac{3}{8}, 0 \right )$

$\left ( \frac{7}{8}, 0 \right )$

Correct answer:

$\left ( -2\frac{1}{3}, 0 \right )$

Explanation:

The -coordinate of the -intercept of a line can be found by substituting 0 for in its equation and solving for :

8y = 3x + 7

$8 \cdot 0 = 3x + 7$

0 = 3x + 7

0 - 7 = 3x + 7 - 7

- 7 = 3x

$- 7 \div 3 = 3x \div 3$

$x = - \frac{7}{3} = -2\frac{1}{3}$

The -intercept is the point $\left ( -2\frac{1}{3}, 0 \right )$ .

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Example Question #664 : Functions And Lines

Give the -intercept of the line of the equation

x= 5y - 17

Possible Answers:

$\left (- \frac{1}{5}, 0 \right )$

(-17, 0)

$\left (3 \frac{2}{5}, 0 \right )$

(5, 0)

$\left ( \frac{5}{17}, 0 \right )$

Correct answer:

(-17, 0)

Explanation:

The -coordinate of the -intercept of a line can be found by substituting 0 for in its equation and solving for :

x= 5y - 17

$x= 5 \cdot 0 - 17 =0 - 17 = -17$

The -intercept is the point (-17, 0) .

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Example Question #665 : Functions And Lines

Give the -intercept of the line of the equation

9y - 4x = 30

Possible Answers:

$\left ( - \frac{3}{10}, 0 \right )$

$\left (- \frac{2}{15}, 0 \right )$

$\left ( - \frac{4}{9}, 0 \right )$

$\left ( - 3 \frac{1}{3}, 0 \right )$

$\left ( -7 \frac{1}{2}, 0 \right )$

Correct answer:

$\left ( -7 \frac{1}{2}, 0 \right )$

Explanation:

The -coordinate of the -intercept of a line can be found by substituting 0 for in its equation and solving for :

9y - 4x = 30

$9 \cdot 0 - 4x = 30$

0 - 4x = 30

- 4x = 30

$- 4x \div (-4) = 30 \div (-4)$

$x =- \frac{30}{4} =- \frac{15}{2} =- 7 \frac{1}{2}$ .

The -intercept is the point $\left ( -7 \frac{1}{2}, 0 \right )$ .

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Example Question #1 : How To Find The Equation Of A Parallel Line

Find a line parallel to

y=2x-4

Possible Answers:

y=-2x-4

y=-2x+4

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

y=2x+4

y=2x-4

Correct answer:

y=2x+4

Explanation:

y=2x+4

A parallel line will have the same value, in this case , as the orignal line but will intercept the y-axis at a different location.

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Example Question #1 : How To Find The Equation Of A Parallel Line

Which of the following lines are parallel to the line defined by the equation:

3y=x-2

Possible Answers:

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

$y=\frac{x}{3}+72$

3y=2x-2

y=x-3

3y=x-7

Correct answer:

$y=\frac{x}{3}+72$

Explanation:

Parallel means the same slope:

3y=x-2

y=mx+b

Solve for :

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

$m=\frac{1}{3}$

Find the linear equation where

$m=\frac{1}{3}$ .

$y=\frac{x}{3}+72$

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Example Question #1 : How To Find The Equation Of A Parallel Line

What is the equation of the line parallel to y=4x+2 that passes through (1,1)?

Possible Answers:

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

y=4x+3

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

y=4x-3

Correct answer:

y=4x-3

Explanation:

The line parallel to y=4x+2 will have the same slope.

The equation for our parallel line will be: $\ y=4x+b$ .

Using the point (1,1) we can solve for the y-intercept:

1=4(1)+b

$\ 1=4+b$

1-4=b

-3=b

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Example Question #1 : How To Find The Equation Of A Parallel Line

Which of these lines is parallel to 4y+2x=6 ?

Possible Answers:

y=-2x+5

y=4x-1

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

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

y=2x-3

Correct answer:

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

Explanation:

Parallel lines have identical slopes. If you convert the given equation to the form y=mx+b , it becomes

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

The slope of this equation is $-\frac{1}{2}$ , so its parallel line must also have a slope of $-\frac{1}{2}$ . The only other line with a slope of $-\frac{1}{2}$ is

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

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Example Question #1 : How To Find The Equation Of A Parallel Line

Which of these lines is parallel to

2y-3x=8?

Possible Answers:

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

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

None of the other answers are correct.

y=3x+4

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

Correct answer:

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

Explanation:

Parallel lines have identical slopes. To determine the slope of the given line, convert it to y=mx+b form:

2y = 3x + 8

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

This line has a slope of $\frac{3}{2}$ .

The only answer choice with a slope of $\frac{3}{2}$ is $y=\frac{3}{2}x-6$ .

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Algebra 1 : Equations of Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #662 : Functions And Lines

Example Question #663 : Functions And Lines

Example Question #23 : How To Find Out If A Point Is On A Line With An Equation

Example Question #664 : Functions And Lines

Example Question #665 : Functions And Lines

Example Question #1 : How To Find The Equation Of A Parallel Line

Example Question #1 : How To Find The Equation Of A Parallel Line

Example Question #1 : How To Find The Equation Of A Parallel Line

Example Question #1 : How To Find The Equation Of A Parallel Line

Example Question #1 : How To Find The Equation Of A Parallel Line

All Algebra 1 Resources

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