Slope of a Line

Slope of a LineA brief tutorial on how to determine the slope of a

line when given the coordinates of two points

on the line

SlopeRemember that the slope of

any line is how much it is slanted and in which direction it slants.

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A line that slants up is said to have positive slope.

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A line that slants down is said to have negative slope.

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A horizontal line is said to have zero slope.

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A horizontal line is said to have zero slope.

A vertical line is said to have undefined slope.

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You’ve completed the section reviewing slope. Before we move on to Section 2 (yep, that was Section 1), let’s take some time to answer a couple of questions to be sure you’re A-OK with Section 1.

Just click on the answer choice you think is correct.

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Question #1

1. The slope of the line on the right is said to be

A. undefinedB. positiveC. negativeD. zero

A. undefinedSorry, this in

incorrect. A line with an undefined slope is a vertical line.

Try Again

View Section 1Tutorial

Go to Question 2

Go to Section 2 Tutorial

B. positive

CORRECT!!!

A line with a positive slope slants upward.


Go to Question 2


C. negativeSorry, this in

incorrect. A line with a negative slope slants downward.

Try Again


Go to Question 2


D. zeroSorry, this in

incorrect. A line with a zero slope is a horizontal line.

Try Again


Go to Question 2


Question #2

1. The slope of the line on the right is said to be

A. undefinedB. positiveC. negativeD. zero

A. undefinedSorry, this in

incorrect. A line with an undefined slope is a vertical line.

Try Again



B. positiveSorry, this is

incorrect. A line with a positive slope slants upward.

Try Again



C. negative

CORRECT!!!A line with a negative

slope slants downward.



D. zeroSorry, this in


Try Again



Finding Slope From Two Points

If given the coordinates of two points, you can find the slope of the line that connects the two points using

m =y2 – y1

x2 – x1

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If given the coordinates of two points, you can find the slope of the line that connects the two points using

m =y2 – y1

x2 – x1

This is called the “slope formula”. The letter “m” is the symbol used for slope.

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m =y2

Find the slope of the line passing through points

– y1

x2 – x1

3,( 2 ) and 6,( 8 )

(6,8)

(3,2)

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m =y2


– y1

x2 – x1

3,( 2 ) and 6,( 8 )

(6,8)

(3,2)

x1 y1 x2 y2

m =––

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m =y2


– y1

x2 – x1

3,( 2 ) and 6,( 8 )

(6,8)

(3,2)

x1 y1 x2 y2

m =––

3 2 6 8

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m =y2


– y1

x2 – x1

3,( 2 ) and 6,( 8 )

(6,8)

(3,2)

x1 y1 x2 y2

m =36

3 2 6 8

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m =y2


– y1

x2 – x1

3,( 2 ) and 6,( 8 )

(6,8)

(3,2)

x1 y1 x2 y2

m =36

3 2 6 8

= 2Repeat section Next


m =y2


– y1

x2 – x1

3,( 2 ) and 6,( 8 )

(6,8)

(3,2)

x1 y1 x2 y2

m =36

3 2 6 8

= 2The slope is positive

The line slants up.

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What if the line is slanting in the other direction?

m =y2 – y1

x2 – x1

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m =y2


– y1

x2 – x1

-5 ,( 7 ) and -2,( 3 )

(-5,7)

(-2,3)

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m =y2


– y1

x2 – x1

x1 y1 x2 y2

m =––

(-5,7)

(-2,3)-5 ,( 7 ) and -2,( 3 )

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m =y2


– y1

x2 – x1

x1 y1 x2 y2

m =––

(-5,7)

(-2,3)-5 ,( 7 ) and -2,( 3 )

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m =y2


– y1

x2 – x1

x1 y1 x2 y2

m = 3

-4

(-5,7)

(-2,3)-5 ,( 7 ) and -2,( 3 )

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m =y2


– y1

x2 – x1

x1 y1 x2 y2

m = = 4

(-5,7)

(-2,3)-5 ,( 7 ) and -2,( 3 )

3The slope is negative

The line slants down. 3

-4

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Now what kind of lesson would this be if you didn’t have to answer some questions?

Just click on the answer choice you think is correct.

Ready?Let’s Go!

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Question #33. Using the coordinates

(6,5) and (2,-3), the slope of the line on the right is

A. -2B. 1/2C. 2D. 1/4

(6,5)

(2,-3)

A. -2Sorry, this in

incorrect. A line with a negative slopes downward.

Try Again


Go to Question 4

(6,5)

(2,-3)

B. ½Sorry, this is

incorrect. The “y” coordinates are in the numerator of the slope formula.

Try Again


Go to Question 4

(6,5)

(2,-3)

C. 2

CORRECT!!


Go to Question 4

(6,5)

(2,-3)

D. 1/4Sorry, this in

incorrect. You must SUBTRACT the coordinates in the slope formula.

Try Again


Go to Question 4

(6,5)

(2,-3)

Question #4

3. Using the coordinates (-2,3) and (3,-2), the slope of the line on the right is

A. 1B. 0C. -1D. 5

(3,-2)

(-2,3)

A. 1Sorry, this in

incorrect. A line that slopes downward has a negative slope.

Try Again


(3,-2)

(-2,3)

B. 0Sorry, this is


Try Again


(3,-2)

(-2,3)

C. 1

CORRECT!!!

Continue to the next

section.

(3,-2)

(-2,3)

D. 5Sorry, this in

incorrect. You must use both the “x” and “y” coordinates in the slope formula.

Try Again


(3,-2)

(-2,3)

Some Simple Keys to Remember

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1. It doesn’t matter which point you pick for x1y1 or x2y2.

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2. If “m” is positive the line slants up.

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3. If “m” is negative the line slants down.

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4. If the numerator of “m” is 0, it’s a horizontal line (zero slope).

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5. If the denominator of “m” is 0, it’s a vertical line (undefined).

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5. If the denominator of “m” is 0, it’s a vertical line (undefined).

6. The larger “m” is, the steeper (or more slanty) the line. Repeat section End

Slope of a Line

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