MTH 070 Elementary Algebra I

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Presentation transcript:

MTH 070 Elementary Algebra I Chapter 3 Linear Equations, Slope, Inequalities, and Introduction to Functions Section 3.2 The Intercept Method Copyright © 2010 by Ron Wallace, all rights reserved.

? Linear Equations Ax + By = C y = mx + b Any equation equivalent in form to … Ax + By = C A, B, & C are constants Standard Form (this section) A second common form … y = mx + b m & b are constants Slope-Intercept From (next section) ?

The amount of gas in your tank as you drive. (0,16) What is significant about these two points? Intercepts! (320,0)

What is true about every point on the x-axis? The y value in the ordered pair is 0. (0,0) (-3,0) (1,0)

What is true about every point on the y-axis? The x value in the ordered pair is 0. (0,2) (0,0) (0,-1)

Intercepts x-intercept: Point where the line crosses the x-axis. (3, 0) y-intercept: Point where the line crosses the y-axis. (0, 2)

Will every line cross both axes? Intercepts x-intercept: Point where the line crosses the x-axis. (3, 0) y-intercept: Point where the line crosses the y-axis. (0, 2) Will every line cross both axes?

Given and Equation Find the Intercepts 2x – 5y = 12 x-intercept: Let y = 0 Solve for x 2x – 5(0) = 12 2x = 12 x = 6 x-intercept: (6, 0) y-intercept: Let x = 0 Solve for y 2(0) – 5y = 12 –5y = 12 y = –12/5 y-intercept: (0, –12/5)

Standard Form Find the Intercepts – Pattern? Ax + By = C x-intercept: Let y = 0 Solve for x Example 7x + 2y = 8 y-intercept: Let x = 0 Solve for y

Using Intercepts to Graph a Line 2x – 5y = 12 x-intercept: (6, 0) y-intercept: (0, -12/5) 1 Check?

Lines that Pass Through the Origin x-intercept? (0,0) y-intercept? What will be true about the equation? Ax + By = C Graphing will require a second point. Lines through the origin: Ax + By = 0 y = mx

Horizontal Lines Horizontal Lines: y = b x-intercept? DNE y-intercept? (0, 2) What will be true about every point on this line? y = 2 … (x, 2) What will be true about the equation? Ax + By = C Horizontal Lines: y = b

Vertical Lines Vertical Lines: x = a x-intercept? (1, 0) y-intercept? DNE What will be true about every point on this line? x = 1 … (1, y) What will be true about the equation? Ax + By = C Vertical Lines: x = a

y = 0 x = 0 One more thing … What is the equation of the x-axis? What is the equation of the y-axis? x = 0