Section 8.3 Using Intercepts to Graph Linear Equations.

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Presentation transcript:

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

Example: Graph 3x + 2y = 6 Set up a T-chart To find the X-interceptTo find the y-intercept Set y= 0Set x = 0______ 3x + 2(0) = 6 3x + 0 = 6 X = 2 3(0) + 2y = y = 6 y = 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-interceptTo find the y-intercept Set y= 0Set x = 0______ 4x - 8(0) = -24 4x - 0 = -24 4x = -24 X = -6 4(0) - 8y = y = y = -24 y = 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 of y = 2x + 3 To find the y-intercept, set x = 0, then solve” y = 2x + 3 y = 2(0) + 3 y = y = 3 To find the x-intercept, set y = 0, then solve: y = 2x + 3 (0) = 2x subtract 3 from both sides -3 = 2x /2 /2divide both sides by 2 X = -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