Section 8.3 Using Intercepts to Graph Linear Equations

X and Y intercepts are the points where a graph crosses the x-axis and the y-axis

This is the x-intercept. At this point, y =0

This is the y-intercept. At this point, x = 0

X and Y intercepts are

the points where a

graph crosses the x-axis and

the y-axis

X and Y intercepts are

the points where a

graph crosses the x-axis and

the y-axis

Example:Graph 3x + 2y = 6

Set up a T-chart

To find the X-intercept To find the y-interceptSet y= 0 Set x = 0______

3x + 2(0) = 63x + 0 = 6X = 2

3(0) + 2y = 60 + 2y = 6y = 3

The x-intercept is (2,0)The y-intercept is (0,3)

4x - 8y = -24

Set up a T-chart

To find the X-intercept To find the y-interceptSet y= 0 Set x = 0______

4x - 8(0) = -244x - 0 = -24 4x = -24X = -6

4(0) - 8y = -240 - 8y = -24-8y = -24y = 3

The x-intercept is (-6,0)The y-intercept is (0,3)

4x - 8y = -24

Whichever intercept you are solving for, cover the other one and for a minute, pretend it’s not there.

Another method -- the “Finger Cover-up Method”

Find the x and y intercepts ofy = 2x + 3

• To find the y-intercept, set x = 0, then solve”y = 2x + 3y = 2(0) + 3y = 0 + 3y = 3

• To find the x-intercept, set y = 0, then solve:y = 2x + 3(0) = 2x + 3-3 -3 subtract 3 from both sides-3 = 2x/2 /2 divide both sides by 2X = -3/2 or -1 ½

Question: Does a linear equation always have a y-intercept?

No. This line is vertical; it never crosses the y-axis. The equation for this line would be x = 5.

What about horizontal lines?

This line is horizontal; it never crosses the x-axis. The equation for this line would be y = 2.

Homework

• Text page 400, #3-5 and #10-18