Graphing Lines How To Find THE SLOPE of a Line Given Two Points How To Find THE SLOPE of a Line...

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Graphing Lines Graphing Lines

Transcript of Graphing Lines How To Find THE SLOPE of a Line Given Two Points How To Find THE SLOPE of a Line...

Page 1: Graphing Lines How To Find THE SLOPE of a Line Given Two Points How To Find THE SLOPE of a Line Given Two Points.

Graphing LinesGraphing Lines

Page 2: Graphing Lines How To Find THE SLOPE of a Line Given Two Points How To Find THE SLOPE of a Line Given Two Points.

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

Page 3: Graphing Lines How To Find THE SLOPE of a Line Given Two Points How To Find THE SLOPE of a Line Given Two Points.

Slope of a Line

x

y

x1 x2

y2

y1

x2 − x1

y2 − y1

m =rise

run=y2 − y1

x2 − x1

x1,y1( )

x2 ,y2( )

Page 4: Graphing Lines How To Find THE SLOPE of a Line Given Two Points How To Find THE SLOPE of a Line Given Two Points.

Slope of a Line

m =rise

run=y2 − y1

x2 − x1

Page 5: Graphing Lines How To Find THE SLOPE of a Line Given Two Points How To Find THE SLOPE of a Line Given Two Points.

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.

Page 6: Graphing Lines How To Find THE SLOPE of a Line Given Two Points How To Find THE SLOPE of a Line Given Two Points.

Find the Slope of the line containing the points

a( ) −3,8( ) and 2,−7( )

b( ) 3.24,0.13( ) and 2.01,−0.07( )

Page 7: Graphing Lines How To Find THE SLOPE of a Line Given Two Points How To Find THE SLOPE of a Line Given Two Points.

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?

Page 8: Graphing Lines How To Find THE SLOPE of a Line Given Two Points How To Find THE SLOPE of a Line Given Two Points.

Graph of a Liney =2x−3

x y

-1 -5

0 -3

1 -1

2 1

3 3

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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).

Page 10: Graphing Lines How To Find THE SLOPE of a Line Given Two Points How To Find THE SLOPE of a Line Given Two Points.

y

xx-intercept

y-intercept

(a,0)

(0,b)

The x and y intercepts of a line

Page 11: Graphing Lines How To Find THE SLOPE of a Line Given Two Points How To Find THE SLOPE of a Line Given Two Points.

Example

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

y =2x−6

Page 12: Graphing Lines How To Find THE SLOPE of a Line Given Two Points How To Find THE SLOPE of a Line Given Two Points.

Slope Intercept Form

y = mx + b

x

y

x − 0

y − b

x,y( )

Any stinkingpoint on the line

m =y − b

x − 0

m =y − b

x

mx = y − b

0,b( )

y-intercept

Page 13: Graphing Lines How To Find THE SLOPE of a Line Given Two Points How To Find THE SLOPE of a Line Given Two Points.

Determine the slope and y-intercept of the following

1( ) y = −x +1

(2) 3x − 4y = 8

Page 14: Graphing Lines How To Find THE SLOPE of a Line Given Two Points How To Find THE SLOPE of a Line Given Two Points.

Point Slope Form

y − y1 = m x − x1( )

x

y

x − x1

y − y1

x,y( )

Any stinkingpoint on the line

m =y − y1x − x1

m x − x1( ) = y − y1

x1,y1( )

Any stinking fixedpoint on the line

Page 15: Graphing Lines How To Find THE SLOPE of a Line Given Two Points How To Find THE SLOPE of a Line Given Two Points.

Find the Equation of the Line Through the Points

1( ) 6,9( ) and 2,−1( )

2( ) −2,1( ) and 2,−1( )

Page 16: Graphing Lines How To Find THE SLOPE of a Line Given Two Points How To Find THE SLOPE of a Line Given Two Points.

Line Formulas

m =y2 − y1

x2 − x1

Slope Formula

y = mx + b Slope Intercept Form

y − y1 = m x − x1( ) Point Slope Form