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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 #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 #3851 : Algebra 1

What is the slope of the following set of coordinates?

(2,0) and (2,1)

Possible Answers:

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

m=0

Undefined

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 #3852 : Algebra 1

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:

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 #161 : 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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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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Example Question #238 : Slope And Line Equations

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 in coordinates and divide this number by the difference between the coordinates.

(12,4)(6,6)

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

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Example Question #571 : Functions And Lines

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 in coordinates and divide this number by the difference between the coordinates.

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

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

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Example Question #572 : Functions And Lines

Find the slope of the equation:

y=5x-9

Possible Answers:

Correct answer:

Explanation:

In order to determine the slope from the given equation we need to make sure that it is written in the following format:

y=mx+b

If the equation of a line is written in the slope-intercept form, then is slope and is the y-intercept.

In this case the slope is:

m=5

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

Find the slope of the equation:

2x+3y=10 ?

Possible Answers:

$\frac{2}{3}$

$-\frac{3}{2}$

$-\frac{2}{3}$

Correct answer:

$-\frac{2}{3}$

Explanation:

In order to determine the slope from the given equation we need to make sure that it is written in the following format:

y=mx+b

If the equation of a line is written in the slope-intercept form, then is slope and is the y-intercept.

In this case we need to convert the equation into slope-intercept form.

2x+3y=10

Subtract from both sides.

3y=10-2x

Divide both sides by .

$y=\frac{10-2x}{3}$

Rewrite.

$y=-\frac{2}{3}x+\frac{10}{3}$

Identify the slope.

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

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Example Question #241 : Slope And Line Equations

Find the slope of the equation:

4y+10=x

Possible Answers:

$-\frac{1}{4}$

$\frac{1}{4}$

Correct answer:

$\frac{1}{4}$

Explanation:

In order to determine the slope from the given equation we need to make sure that it is written in the following format:

y=mx+b

If the equation of a line is written in the slope-intercept form, then is slope and is the y-intercept.

In this case we need to convert the equation into slope-intercept form.

4y+10=x

Subtract from both sides.

4y=x-10

Divide both sides by .

$y=\frac{x-10}{4}$

Identify the slope.

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

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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 #165 : How To Find Slope Of A Line

Example Question #3851 : Algebra 1

Example Question #3852 : Algebra 1

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

Example Question #237 : Slope And Line Equations

Example Question #238 : Slope And Line Equations

Example Question #571 : Functions And Lines

Example Question #572 : Functions And Lines

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

Example Question #241 : Slope And Line Equations

All Algebra 1 Resources

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