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Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #155 : How To Find Slope Of A Line

Find the slope of the line if the line connects the points (5,-1) and (-9,9) .

Possible Answers:

$-\frac{5}{2}$

$\frac{5}{7}$

$-\frac{5}{7}$

Correct answer:

$-\frac{5}{7}$

Explanation:

Write the formula for the slope.

$m= \frac{y_2-y_1}{x_2-x_1}$

Substitute the points.

$m= \frac{9-(-1)}{-9-5} = \frac{10}{-14}$

Reduce the fraction.

$m= -\frac{5}{7}$

The slope is $-\frac{5}{7}$ .

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Example Question #156 : How To Find Slope Of A Line

Find the slope of the following line:

18y = -72x + 36

Possible Answers:

Correct answer:

Explanation:

To find the slope of a line, we will write it in slope-intercept form

y = mx + b

where m is the slope. Given the line

18y = -72x + 36

we will need to solve for y, or get y to stand alone. To do that, we will divide each term by 18. So,

$\frac{18y}{18} = \frac{-72x}{18} + \frac{36}{18}$

y = -4x + 2

Using the information given above, we can see that the slope is -4.

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Example Question #157 : How To Find Slope Of A Line

What is the slope of the line 3x-y+6=3x ?

Possible Answers:

$\textup{Slope does not exist.}$

Correct answer:

Explanation:

To find the slope of the line, we will need to re-format the equation back to slope-intercept form, y=mx+b .

Add on both sides.

3x-y+6+y=3x+y

3x+6=3x+y

Subtract on both sides.

3x+6-3x=3x+y-3x

Simplify both sides.

y=6

This is a horizontal line and the value of is zero.

The answer of the slope is:

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Example Question #158 : How To Find Slope Of A Line

Give the slope of the line of the equation

3x+2= 6y

Possible Answers:

$\frac{1}{3}$

$\frac{1}{2}$

Correct answer:

$\frac{1}{2}$

Explanation:

Rewrite the equation in slope-intercept form y = mx+b :

3x+2= 6y

6y = 3x+2

$6y \div 6 = (3x+2) \div 6$

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

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

The coefficient of , which is $\frac{1}{2}$ , is the slope of the line.

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Example Question #159 : How To Find Slope Of A Line

Give the slope of the line of the equation

8y = 3x + 7

Possible Answers:

$\frac{3}{7}$

$\frac{7}{8}$

$\frac{3}{8}$

$\frac{8}{3}$

$\frac{7}{3}$

Correct answer:

$\frac{3}{8}$

Explanation:

Rewrite the equation in slope-intercept form y = mx+b :

8y = 3x + 7

$8y \div 8 = (3x + 7) \div 8$

$y = \frac{3}{8}x+ \frac{7}{8}$

The coefficient of , which is $\frac{3}{8}$ , is the slope of the line.

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Example Question #160 : How To Find Slope Of A Line

Give the slope of the line of the equation

7y+ 4x = 29

Possible Answers:

$\frac{29}{7}$

$\frac{29}{4}$

$\frac{7}{29}$

$-\frac{7}{4}$

$-\frac{4}{7}$

Correct answer:

$-\frac{4}{7}$

Explanation:

Rewrite the equation in slope-intercept form y = mx+b :

7y+ 4x = 29

7y+ 4x - 4x = 29 - 4x

7y = -4x+ 29

$7y \div 7 = (-4x+ 29) \div 7$

$y = -\frac{4}{7}x + \frac{29}{7}$

The coefficient of , which is $-\frac{4}{7}$ , is the slope of the line.

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Example Question #222 : Slope And Line Equations

Give the slope of the line of the equation

9y - 4x = 30

Possible Answers:

$\frac{9}{4}$

$-\frac{4}{9}$

$-\frac{9}{4}$

$\frac{4}{9}$

Correct answer:

$\frac{4}{9}$

Explanation:

Rewrite the equation in slope-intercept form y = mx+b :

9y - 4x = 30

9y - 4x + 4x = 30+ 4x

9y = 4x+ 30

$9y \div 9 = (4x+ 30) \div 9$

$y = \frac{4}{9} x + \frac{30}{9}$

$y = \frac{4}{9} x + \frac{10}{3}$

The coefficient of , which is $\frac{4}{9}$ , is the slope.

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Example Question #231 : Slope And Line Equations

Give the slope of the line of the equation

x= 5y - 17

Possible Answers:

$\frac{1}{5}$

$-\frac{1}{5}$

The line has no slope

Correct answer:

$\frac{1}{5}$

Explanation:

Rewrite the equation in slope-intercept form y = mx+b :

x= 5y - 17

5y - 17 = x

5y - 17 + 17 = x + 17

5y = x + 17

$5y \div 5 = (x + 17) \div 5$

$y= \frac{1}{5}x + \frac{17 }{5}$

The coefficient of , which is $\frac{1}{5}$ , is the slope.

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Example Question #232 : Slope And Line Equations

Give the slope of the line of the equation

7x + 6y = 33

Possible Answers:

$\frac{7}{6}$

$-\frac{6}{7}$

The correct answer is not among the other choices.

$\frac{6}{7}$

$-\frac{7}{6}$

Correct answer:

$-\frac{7}{6}$

Explanation:

Rewrite the equation in slope-intercept form y = mx+b :

7x + 6y = 33

7x + 6y - 7x = 33- 7x

6y = -7x + 33

$6y \div 6 =( -7x + 33) \div 6$

$y = -\frac{7}{6}x + \frac{33}{6}$

The coefficient of , which is $-\frac{7}{6}$ , is the slope.

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Example Question #233 : Slope And Line Equations

Find the slope of a line given by the equation:

y=2(2x-3)+4x

Possible Answers:

$\textup{Slope is unknown.}$

Correct answer:

Explanation:

In order to find the slope of this equation, we will need to put this in y-intercept form, y=mx+b .

Simplify the equation by distribution and combine like-terms.

y=2(2x)+2(-3)+4x

Simplify the parentheses.

y=4x-6+4x

Add like terms.

y=8x-6

The slope is .

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Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #155 : How To Find Slope Of A Line

Example Question #156 : How To Find Slope Of A Line

Example Question #157 : How To Find Slope Of A Line

Example Question #158 : How To Find Slope Of A Line

Example Question #159 : How To Find Slope Of A Line

Example Question #160 : How To Find Slope Of A Line

Example Question #222 : Slope And Line Equations

Example Question #231 : Slope And Line Equations

Example Question #232 : Slope And Line Equations

Example Question #233 : Slope And Line Equations

All Algebra 1 Resources

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