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Algebra 1 : Equations of Lines

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Example Questions

Example Question #151 : How To Find Slope Of A Line

Give the slope of the line of the equation

7y+ 4x = 29

Possible Answers:

$\frac{29}{7}$

$-\frac{7}{4}$

$\frac{29}{4}$

$\frac{7}{29}$

$-\frac{4}{7}$

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 #161 : How To Find Slope Of A Line

Give the slope of the line of the equation

9y - 4x = 30

Possible Answers:

$-\frac{4}{9}$

$\frac{9}{4}$

$\frac{4}{9}$

$-\frac{9}{4}$

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:

$\frac{1}{5}$

The line has no slope

$-\frac{1}{5}$

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:

$-\frac{7}{6}$

The correct answer is not among the other choices.

$\frac{6}{7}$

$\frac{7}{6}$

$-\frac{6}{7}$

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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Example Question #165 : How To Find Slope Of A Line

Given the following equation, $\frac{1}{3}x+\frac{1}{4}y=1$ , what is the slope of this line?

Possible Answers:

$\frac{4}{3}$

$\frac{1}{3}$

$\frac{1}{12}$

$-\frac{3}{4}$

$-\frac{4}{3}$

Correct answer:

$-\frac{4}{3}$

Explanation:

The given equation is currently in standard form. In order to find the slope, we will need to isolate the variable and put the equation in slope-intercept form.

The slope-intercept form is: y=mx+b

Subtract $\frac{1}{3}x$ from both sides.

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

Simplify both sides.

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

Multiply by four on both sides.

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

Distribute both sides.

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

Rearrange the terms.

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

The slope is: $-\frac{4}{3}$

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Example Question #234 : Slope And Line Equations

What is the slope of the following set of coordinates?

(2,0) and (2,1)

Possible Answers:

m=0

Undefined

$m=\frac{1}{2}$

m=1

m=2

Correct answer:

Undefined

Explanation:

To solve this problem you need to know the slope formula and set it up accordingly:

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

$\frac{1-0}{2-2}$

This simplifies to:

$\frac{1}{0}$ and because 0 is in the denominator this slope is undefined.

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Example Question #235 : Slope And Line Equations

Find the slope of a line if the points given are (6,9) and (-3,6) .

Possible Answers:

$\frac{1}{3}$

$\frac{3}{2}$

$-\frac{3}{2}$

$-\frac{1}{3}$

Correct answer:

$\frac{1}{3}$

Explanation:

Write the formula to find the slope given two points.

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

Substitute the given points into this formula.

$m=\frac{6-9}{-3-6}$

Simplify this fraction and reduce.

$m=\frac{-3}{-9}= \frac{1}{3}$

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Example Question #321 : Equations Of Lines

Points A: (3,2) and B: (4,2) lie on the same line. What is the slope of this line?

Possible Answers:

Undefined

Correct answer:

Explanation:

The slope equation is:

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

Plugging these points:

$\frac{2-2}{4-3}$

$\frac{0}{1}=0$

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Example Question #237 : Slope And Line Equations

Find the slope between the following coordinate points:

(2,3) and (4,5)

Possible Answers:

$\frac{1}{2}$

$\frac{1}{6}$

$\frac{1}{4}$

Correct answer:

Explanation:

In order to find the slope, we must find the difference in coordinates and divide this number by the difference between the coordinates.

(2,3)(4,5)

$\text{Slope}=\frac{5-3}{4-2}=\frac{2}{2}=1$

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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 #151 : How To Find Slope Of A Line

Example Question #161 : How To Find Slope Of A Line

Example Question #231 : Slope And Line Equations

Example Question #232 : Slope And Line Equations

Example Question #233 : Slope And Line Equations

Example Question #165 : How To Find Slope Of A Line

Example Question #234 : Slope And Line Equations

Example Question #235 : Slope And Line Equations

Example Question #321 : Equations Of Lines

Example Question #237 : Slope And Line Equations

All Algebra 1 Resources

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