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Section 3.2 Graphing Linear Equations 217 4b. The equation x = -3 can be written as x + 0y = -3. Notice that for any y-value chosen, x is -3. So, any ordered pair whose x-coordinate is -3 is a solution. If y = 0, 1, and -1, the ordered pair solutions are x y (x, y) -3 0 (3, 0) -3 1 (3, 1) -3 -1 (-3, -1) The graph is a vertical line with an x-intercept of (-3, 0). Note the graph does not have a y-intercept because the x-coordinate is never zero. 4c. The equation 2x + 5 = 0 can be written as 2x + 0y = -5 or as x + 0y=- 5 2 . Notice that for any y-value chosen, x is - 5 2 . So, any ordered pair whose x-coordinate is - 5 2 is a solution. If y = 1, -4, and 3, the ordered pair solutions are x y (x, y) - 5 2 1 a- 5 2 , 1b - 5 2 -4 a- 5 2 , -4b - 5 2 3 a- 5 2 , 3b The graph is a vertical line with x-intercept a- 5 2 , 0b . Notice the line has no y-intercept since the x-coordinate is never zero. Student Check 4 Graph each linear equation. a. y = -1 b. x = 5 c. 3y + 2 = 0 Applications In the application problems encountered in this section, we will be given a linear equation that models a real-world situation. We will construct the graph of the equation and extract information from the equation. �� ������������������������ ������������������ Use the equation to answer each question. 5a. The median annual income for men with a bachelor’s degree can be modeled by the equation y = 1443x + 38,843, where x is the number of years after 1990. (Source: www.infoplease.com) i. Is this equation a linear equation in two variables? Why or why not? ii. Find the y-intercept of the equation and interpret its meaning in the context of this problem. iii. Find the x-intercept of the equation and interpret its meaning in the context of this problem. iv. Find the median annual income for the years 2000 and 2010. Objective 5 ▶ Solve application problems. 2 4 2 4 –2 –4 –2 –4 x y (–3, 0) 2 4 2 4 –2 –4 –2 –4 x y 52, 0 –


hendricks_beginning_algebra_1e_ch1_3
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