Section 3.2 Graphing Linear Equations 215 3c. x y (x, y) 2x - 0 = 0 2x = 0 2x = 2 0 2 x = 0 0 (0, 0) 0 2(0) - y = 0 -y = 0 -y = -1 0 -1 y = 0 (0, 0) 2 2(2) - y = 0 4 - y = 0 4 - y - 4 = 0 - 4 -y = -4 -y = -1 -4 -1 y = 4 (2, 4) The x- and y-intercepts for this graph are the same point, the origin. So, we need to find another point on the graph to have enough information to draw the line. Choose any value for x and solve for y. Plotting (0, 0) and (2, 4) gives us the graph of 2x - y = 0. (2, 4) (0, 0) 4 2 2 4 –2 –4 –2 –4 x y ������������ Equations of the form Ax + By = 0 have graphs that go through the origin since (0, 0) is always a solution of this type of equation. Student Check 3 Find the x- and y-intercepts for each equation. Use these points to graph each line. a. 4x - y = -8 b. y = 3x - 3 c. 4x + y = 0 Horizontal and Vertical Lines Horizontal and vertical lines are special cases of linear equations in two variables. Consider the graph of the horizontal line shown next. (2, 3) (0, 3) (–4, 3) (1, 3) 2 2 4 –2 –4 –2 –4 x y Objective 4 ▶ Recognize and graph horizontal and vertical lines.
hendricks_beginning_algebra_1e_ch1_3
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