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 –
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