AlgebraAlgebra

4.2 4.2

Graphing Equations of LinesGraphing Equations of Lines

Slope-Intercept Form

y = mx + b

slope y-intercept

where the line crosses the y axis

riserun

•The y - intercept (b) is the point where the line crosses the y axis.

•For example:In the equation y = 2x – 5

Y - intercept

The y-intercept is -5So the line crosses the y-axis at the point (0, -5)

•The slope (m) is a number that describes the whether the line goes uphill or downhill.

•Positive slope UPHILL line•Negative slope DOWNHILL line

•For example, in the equation y = 2x - 5

Slope

The slope is positive 2The line is uphill

•The slope (m) also describes the steepness of the line as the ratio RISE .

RUN

•For example, in the equation y = 2x - 5

Slope

The slope is 2 so the line

RISES 2 from point to point

RUNS 1

Slope and y - interceptEquation Slope rise

runUphill or downhill

Y = 3x - 2

Y = - 1 x + 4 3

Y = 3 x + 6 4

Y = - 5 x – 3 2

3

-1 3

34

-5 2

Uphill

Downhill

Uphill

Downhill

31

-1 3

34

-5 2

y - intercept

-2

4

6

-3

You have previously graphed using an X/Y Table.

x y

y = 2x + 3

2 7

1 5

0 3

-1 1

.(2,7) .(0,3)

.(1,5)

.(-1,1)x

y

This is the graph of the equation y = 2x + 3

Today you will learn an easy method of graphing that

uses only the y-intercept (b) and the slope (m).

Graphing the y-intercept

y = 2x + 3.(0,3)

x

y

The y intercept of the line is 3.Plot the point (0,3) on the y axis.

Using the slope to find more points

y = 2x + 3 .(0,3)

.(1,5)

x

y

The slope of the line is 2 or

From the point (0,3) use the graph paper to:rise 2 (go up by 2) and run 1 (go right by 1). This takes you to the point (1,5)

rise 2

run 1

Rise 2Run 1

Using the slope to find more points

.(0,3)

.(1,5)

x

y

From the point (1,5) use the graph paper to:rise 2 (go up by 2) and run 1 (go right by 1). This takes you to the point (2,7)

rise 2

run 1

.(2,7)

Rise 2Run 1

.(0,3)

.(1,5)

x

y

.(2,7)

Connect the three points to graph the line

y = 2x + 3

Graphing the Equation for a Line

STEPS

1. Get the equation in Slope-Intercept Form

y = mx + b

Isolate the y slope y-intercept

Graphing the Equation for a Line

STEPS

2. Plot the y-intercept

3. Use the slope to plot at least two more points (rise, run, plot…..repeat)

4. Connect the points as a line

5. Test a point

Now try graphing some equations of your own

using a graphing website

http://www.webmath.com/gline.html

HomeworkHomework

Go srvhs.org and link to my website

Find the link for the Algebra “Graphing Lines Using Slope-Intercept Form” Assignment

Graph 30 lines. Print out your final graph. Keep a tally and have your parent sign off on the sheet that you graphed 30 lines using the animated software.