Section 3.2 Linear Equations in Two Variables 209 Answers 10. (0, 0) 11. (0, 0) 12. 5 4 3 2 1 y 54 3 2 1 1 2 3 4 5 1 2 3 4 5 x c. Because the x-intercept and the y-intercept are the same point (the origin), one or more additional points are needed to graph the line. In the table, we have arbitrarily selected additional values for x and y to find two more points on the line. 4x 5y 0 4x 5y 0 4152 5y 0 4x 5122 0 20 5y 0 4x 10 0 5y 20 4x 10 1 52 x x 10 4 5 2 152 15, 42 , 22 52 , 22 1 , 22. 5 4 3 2 1 Let x 5: Let y 2: 1212 , 22 543 21 1 2 3 4 5 1 2 3 4 5 (5, 4) (0, 0) y x (2 , 2) 12 Figure 3-10 y 4 x y 5 4 2 52 0 0 is a solution. The line through the ordered pairs (0, 0), , and is shown in Figure 3-10. Note that the point can be written as The line represents the set of all solutions to the equation 4x 5y 0. Skill Practice Given the equation , 10. Find the x-intercept. 11. Find the y-intercept. 12. Graph the equation. (Hint: You may need to find an additional point.) 4. Horizontal and Vertical Lines Recall that a linear equation can be written in the form of Ax By C, where A and B are not both zero. However, if A or B is 0, then the line is either horizontal or vertical. A horizontal line either lies on the x-axis or is parallel to the x-axis.A vertical line either lies on the y-axis or is parallel to the y-axis. 2x 3y 0 x y 2 5 15, 42 is a solution. Equations of Vertical and Horizontal Lines 1. A vertical line can be represented by an equation of the form where k is a constant. 2. A horizontal line can be represented by an equation of the form where k is a constant. x k, y k, Avoiding Mistakes Do not try to graph a line given only one point. There are infinitely many lines that pass through a single point.
miller_beginning_intermediate_algebra_4e_ch1_3
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