Graphing LinesGraphing Lines

How To Find How To Find THE SLOPETHE SLOPE of of a Line Given Two Pointsa Line Given Two Points

Slope of a Line

x

y

x1 x2

y2

y1

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x2 − x1

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y2 − y1

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m =rise

run=y2 − y1

x2 − x1

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x1,y1( )

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x2 ,y2( )

Slope of a Line

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m =rise

run=y2 − y1

x2 − x1

Definition of Slope

• The slope of the line is it’s measure of steepness. It measures the rate of change of the line. In all lines the slope is constant, it doesn’t change no matter where you are at on the line.

Find the Slope of the line containing the points

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a( ) −3,8( ) and 2,−7( )

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b( ) 3.24,0.13( ) and 2.01,−0.07( )

BicyclesIn groups, generate the line that relates the number of wheels to the number of bicycles. Represent it Graphically.

What does the slope of this line represent?

Graph of a Liney =2x−3

x y

-1 -5

0 -3

1 -1

2 1

3 3

Intercepts

• Where the graph crosses the x-axis is the x-intercept. It has coordinates (a,0).

• Where the graph crosses the y-axis is the y-intercept. It has coordinates (0,b).

y

xx-intercept

y-intercept

(a,0)

(0,b)

The x and y intercepts of a line

Example

• Find the x and y intercepts of the line given by:

y =2x−6

Slope Intercept Form

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y = mx + b

x

y

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x − 0

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y − b

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x,y( )

Any stinkingpoint on the line

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m =y − b

x − 0

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m =y − b

x

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mx = y − b

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0,b( )

y-intercept

Determine the slope and y-intercept of the following

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1( ) y = −x +1

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(2) 3x − 4y = 8

Point Slope Form

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y − y1 = m x − x1( )

x

y

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x − x1

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y − y1

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x,y( )

Any stinkingpoint on the line

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m =y − y1x − x1

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m x − x1( ) = y − y1

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x1,y1( )

Any stinking fixedpoint on the line

Find the Equation of the Line Through the Points

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1( ) 6,9( ) and 2,−1( )

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2( ) −2,1( ) and 2,−1( )

Line Formulas

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m =y2 − y1

x2 − x1

Slope Formula

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y = mx + b Slope Intercept Form

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y − y1 = m x − x1( ) Point Slope Form