Graphing Linear Equations

In Slope-Intercept Form

We have already seen that linear equations have two variables and when we plot all the (x,y) pairs that make the equation true we get a line.

In this section, instead of making a table, evaluating y for each x, plotting the points and making a line, we will use The Slope-Intercept Form of the equation to graph the line.

y 2x 1

y 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 3

2x 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 3

2x 2

using their y-intercepts and slopes.

y 2x 1

1) 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 3

2x 2

right 2

up 3

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

2x y 3

y 2x 3

The constant, b = 3 is the y-intercept.

The coefficient, m = -2 is the slope.

x2 x2

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

Let’s Practice

35

3 xy 13 xy

1027 yx 124 yx

HW

• pg. 297 #2,4,6,8,10

• pg. 298 #12 to 26 even