Graphing Linear Equations

In Slope-Intercept Form

In order to graph using point plotting, you will need to create a table.

You will need to choose at least 3 numbers for x and “plug” them into the equation to find corresponding y values.

For Example:Graph y = 2x - 1

x yChoose x values

“plug” x into the equation

Plot the points

-1 2(-1)-1=-30 2(0)-1 = -11 2(1)-1 = 1

Graph using point plotting321

xy

x y

-2

0

2

21

21

21

(-2) + 3 = 2

(0) + 3 = 3

(2) + 3 = 4

y 2x 1y x 4

y 32

x 2

These equations are all in Slope-Intercept Form:

Notice that these equations are all solved for y.

Just by looking at an equation in this form, we can draw the line (no tables).

•The constant is the y-intercept. •The coefficient is the slope.

y 2x 1

y x 4

y 32

x 2

Constant = 1, y-intercept = 1.

Coefficient = 2, slope = 2.

Constant = -4, y-intercept = -4.

Coefficient = -1, slope = -1.

Constant = -2, y-intercept = -2.

Coefficient = 3/2, slope = 3/2.

The formula for Slope-Intercept Form is:

y mx b;• ‘b’ is the y-intercept. • ‘m’ is the slope.

On the next three slides we will graph the three equations:

y 2x 1, y x 4, y 32

x 2

using their y-intercepts and slopes.

y 2x 11) Plot the y-intercept as a point on the y-axis. The constant, b = 1, so the y-intercept = 1.

2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = 2, so the slope = 2/1.

up 2

right 1 up 2

right 1

1) Plot the y-intercept as a point on the y-axis. The constant, b = -4, so the y-intercept = -4.

2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = -1, so the slope = -1/1.

right 1down 1

right 1

y x 4

down 1

1) Plot the y-intercept as a point on the y-axis. The constant, b = -2, so the y-intercept = -2.

2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = 3/2, so the slope = 3/2.

right 2

up 3

y 32

x 2

right 2

up 3

Sometimes we must solve the equation for y before we can graph it.

2x y 3

2x y ( 2x) ( 2x) 3

y 2x 3

The constant, b = 3 is the y-intercept.The coefficient, m = -2 is the slope.

1) Plot the y-intercept as a point on the y-axis. The constant, b = 3, so the y-intercept = 3.

2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = -2, so the slope = -2/1.

right 1down 2

right 1

down 2

y 2x 3

Important!!!This is one of the big concepts in

Algebra. You need to thoroughly understand this!

Slope – Intercept Formy = mx + b

m represents the slopeb represents the y-intercept

Graphing Using the Slope-Intercept Form

To graph a linear equation, you will need to find the slope and the y-intercept for the equation.

Remember: y = mx + b

slope Y-intercept (the point where the graph crosses the y-axis)

Graph 132

xy Slope =

Y-intercept =

32

1

1. Plot the y-intercept

2. Use the slope to find the next point

Slope = “rise over run”

Graph 2x + 5y = 10 using the slope-intercept form: (put the equation in slope-intercept form first)

2x + 5y = 10

5y = 10 – 2x

y = 2 – 2/5 x

slope = -2/5y – intercept = 2

A negative slope means you will go down then right from the y-intercept