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Algebra 1 : Slope and Line Equations

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Example Questions

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Example Question #162 :How To Find Slope Of A Line

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 #163 :How To Find Slope Of A Line

Give the slope of the line of the equation

7x + 6y = 33

Possible Answers:

$-\frac{7}{6}$

$\frac{6}{7}$

$\frac{7}{6}$

The correct answer is not among the other choices.

$-\frac{6}{7}$

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 #161 :How To Find Slope Of A Line

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:

$-\frac{3}{4}$

$\frac{1}{3}$

$\frac{4}{3}$

$-\frac{4}{3}$

$\frac{1}{12}$

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 thevariable 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 #166 :How To Find Slope Of A Line

What is the slope of the following set of coordinates?

(2,0) and (2,1)

Possible Answers:

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

m=1

m=2

Undefined

m=0

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 #167 :How To Find Slope Of A Line

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

Possible Answers:

$-\frac{1}{3}$

$\frac{1}{3}$

$-\frac{3}{2}$

$\frac{3}{2}$

Correct answer:

$\frac{1}{3}$

Explanation:

编写公式斜率给定两个效果ts.

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

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 #168 :How To Find Slope Of A Line

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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例子问题# 169:How To Find Slope Of A Line

Find the slope between the following coordinate points:

(2,3) and (4,5)

Possible Answers:

$\frac{1}{2}$

$\frac{1}{4}$

$\frac{1}{6}$

Correct answer:

Explanation:

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

(2,3)(4,5)

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

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Example Question #170 :How To Find Slope Of A Line

Find the slope between the following coordinate points:

(12,4) and (6,6)

Possible Answers:

$-\frac{1}{3}$

$\frac{1}{3}$

Correct answer:

$-\frac{1}{3}$

Explanation:

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

(12,4)(6,6)

$\text{Slope}=\frac{6-4}{6-12}=\frac{2}{-6}=-\frac{1}{3}$

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Example Question #171 :How To Find Slope Of A Line

Find the slope between the following coordinate points:

(-3,-5) and (-16,8)

Possible Answers:

$-\frac{1}{2}$

$\frac{1}{2}$

Correct answer:

Explanation:

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

(-3,-5)(-16,8)

$\text{Slope}=\frac{8-(-5)}{-16-(-3)}=\frac{13}{-13}=-1$

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Algebra 1 : Slope and Line Equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #162 :How To Find Slope Of A Line

Example Question #163 :How To Find Slope Of A Line

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

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

Example Question #166 :How To Find Slope Of A Line

Example Question #167 :How To Find Slope Of A Line

Example Question #168 :How To Find Slope Of A Line

例子问题# 169:How To Find Slope Of A Line

Example Question #170 :How To Find Slope Of A Line

Example Question #171 :How To Find Slope Of A Line

All Algebra 1 Resources

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