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Algebra 1 : Slope and Line Equations

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Example Questions

Example Question #121 : How To Find Slope Of A Line

Line

You have a line which connects two points. Each point is represented as an (x,y) pair. Find the slope of the line for points shown in the figure where the points are

(A) (-2,3)

(B) (3,-1)

Possible Answers:

slope=-0.8

slope=0.8

slope=-1.25

slope=1.25

Correct answer:

slope=-0.8

Explanation:

The slope can be found between two points by finding the change in values divided by the change in values.

$slope=\frac{\Delta y}{\Delta x}$

which is often referred to as rise over run,

Ror

You can actually use any two points along the line to find the slope as long as the line is linear (straight line). Taking the end points since they are given is a convenient way of doing it.

$slope=\frac{\Delta y}{\Delta x}=\frac{(B)_{y}-(A)_{y}}{(B)_{x}-(A)_{x}}$

$slope=\frac{-1-3}{3-(-2)}=\frac{-4}{5}$

So the slope of this line segment is -0.8

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Example Question #121 : How To Find Slope Of A Line

Find the slope of the following line:

-8y = 24x - 16

Possible Answers:

Correct answer:

Explanation:

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

y = mx+ b

where is the slope.

So, in the equation

-8y = 24x - 16

we will solve for y and get it by itself. To do that, we will divide each term by .

$\frac{-8y}{-8} = \frac{24x}{-8} - \frac{16}{-8}$

y = -3x + 2

Looking at this equation, we can see is the slope.

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Example Question #124 : How To Find Slope Of A Line

What is the slope of a line with points (2,8) and (3,-2) .

Possible Answers:

$\frac{11}{4}$

Correct answer:

Explanation:

Write the formula for slope.

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

Either choice will yield the same slope. Let's use the first equation.

$m=\frac{y_1-y_2}{x_1-x_2} = \frac{8-(-2)}{2-3}$

Simplify to find the slope.

$\frac{8-(-2)}{2-3} =\frac{10}{-1}=-10$

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Example Question #121 : How To Find Slope Of A Line

You know that a line has the following points:

(9,4) and (12,8)

Calculate the slope of the line.

Possible Answers:

$\frac{4}{3}$

$\frac{3}{4}$

$-\frac{3}{4}$

$-\frac{4}{3}$

Correct answer:

$\frac{4}{3}$

Explanation:

The slope (m) of a line can be solved if you know at least two points that fall on the line using the following equation:

$m = \frac{y1-y2}{x1-x2}$

The coordinates are always written second when looking at coordinate pairs, and therefore the coordinates are first. We can thus insert our given points into this equation:

$m = \frac{4-8}{9-12}$

$m = \frac{-4}{-3}$

$m = \frac{4}{3}$

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Example Question #121 : How To Find Slope Of A Line

Find the slope of the line connecting the following two points:

(99,156) (44,101)

Possible Answers:

Correct answer:

Explanation:

Find the slope of the line connecting the following two points:

(99,156) (44,101)

Find slope with the following formula:

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

$m=\frac{156-101}{99-44}=\frac{55}{55}=1$

so our slope is simply 1

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Example Question #127 : How To Find Slope Of A Line

Find the slope of 2x-3y=19 .

Possible Answers:

$\frac{3}{2}$

$-\frac{2}{3}$

$\frac{2}{3}$

Correct answer:

$\frac{2}{3}$

Explanation:

In order to find the slope, we need to put the following equation in slope intercept form.

y=mx+b

The represents the slope.

Subtract on both sides.

2x-3y-2x=19-2x

Simplify the left side and reorganize the right.

-3y=-2x+19

Divide by negative three on both sides.

$\frac{-3y}{-3}=\frac{-2x+19}{-3}$

Simplify both sides.

$y=\frac{2}{3}x-\frac{19}{3}$

The slope is $\frac{2}{3}$ .

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Example Question #121 : How To Find Slope Of A Line

Find the slope of the following line:

2x+3y=5

Possible Answers:

$\frac{2}{3}$

$\frac{3}{2}$

$\frac{-3}{2}$

$\frac{-2}{3}$

Correct answer:

$\frac{-2}{3}$

Explanation:

In order to find the slope of this line, it needs to be converted from standard form into slope-intercept form. To do this solve for "y".

2x+3y=5

3y=-2x+5

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

The slope is the number in front of the "x" which in this case is -2/3

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Example Question #121 : How To Find Slope Of A Line

Find the slope of the following line:

x-y=6

Possible Answers:

$\frac{1}{6}$

Correct answer:

Explanation:

In order to find the slope of this line, it needs to be converted from standard form into slope-intercept form. To do this solve for "y".

x-y=6

-y=-x+6

y=x-6

The slope is the number in front of the "x" which in this case is 1

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Example Question #121 : How To Find Slope Of A Line

Find the slope of the following line:

3x+y=4

Possible Answers:

$\frac{3}{4}$

Correct answer:

Explanation:

In order to find the slope of this line, it needs to be converted from standard form into slope-intercept form. To do this solve for "y".

3x+y=4

y=-3x+4

The slope is the number in front of the "x" which in this case is -3

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Example Question #291 : Equations Of Lines

Find the slope of the following line:

-x+2y=2

Possible Answers:

$\frac{1}{2}$

$\frac{-1}{2}$

Correct answer:

$\frac{1}{2}$

Explanation:

In order to find the slope of this line, it needs to be converted from standard form into slope-intercept form. To do this solve for "y".

-x+2y=2

2y=x+2

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

The slope is the number in front of the "x" which in this case is 1/2

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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 #121 : How To Find Slope Of A Line

Example Question #121 : How To Find Slope Of A Line

Example Question #124 : How To Find Slope Of A Line

Example Question #121 : How To Find Slope Of A Line

Example Question #121 : How To Find Slope Of A Line

Example Question #127 : How To Find Slope Of A Line

Example Question #121 : How To Find Slope Of A Line

Example Question #121 : How To Find Slope Of A Line

Example Question #121 : How To Find Slope Of A Line

Example Question #291 : Equations Of Lines

All Algebra 1 Resources

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