Section 3.2 Graphing Linear Equations 211 ������������ The graph of any linear equation in two variables is a line. ���������������������� Graphing a Linear Equation in Two Variables by Plotting Points Step 1: Make a table of at least three ordered pairs that satisfy the equation. Only two ordered pairs are required to graph a line, but a third point is good to use as a check. a. To get the solutions, choose a value for x, substitute this in the equation and solve for y. (A good idea is to use a negative value, zero, and a positive value.) b. We can also choose a value for y, substitute this in the equation, and solve for x. Step 2: Plot the three ordered pairs. These three points should lie in a straight line. If they do not, an error has been made. Recheck your work. Step 3: Draw the line that contains the three points. The line should extend beyond the points and have arrows at both ends to indicate that there are infinitely many solutions of the equation. �� ������������������������ ������������������ Graph each linear equation. 2a. y = -x + 3 2b. y = 4 3 x - 4 2c. x - 2y = 4 Solutions 2a. Let x = -1, 0, and 1. We will use the table to organize our work to obtain the solutions. x y = -x + 3 (x, y) -1 y = -(-1) + 3 y = 1 + 3 y = 4 (-1, 4) 0 y = -(0) + 3 y = 0 + 3 y = 3 (0, 3) 1 y = -(1) + 3 y = -1 + 3 y = 2 (1, 2) Plot the points (-1, 4), (0, 3), and (1, 2). Since these points lie on a line, we draw a line through the points to obtain the graph of y = -x + 3. (–1, 4) (0, 3) 2 –4 –2 2 x 6 4 6 –2 y (1, 2)
hendricks_beginning_algebra_1e_ch1_3
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