244 Chapter 3 Linear Equations in Two Variables Graph Parallel and Perpendicular Lines In Section 3.5, we will determine equations of lines that go through particular points that are parallel or perpendicular to a given line. It is helpful to visualize this situation before writing their equations. ���������������������� Graphing a Line through a Point That Is Parallel or Perpendicular to a Given Line Step 1: Determine the slope of the given line. Step 2: Determine the slope of the parallel or perpendicular line. a. The slope of the parallel line is equal to the slope of the given line. b. The slope of the perpendicular line is equal to the negative reciprocal of the slope of the given line. Step 3: Graph the given line using its slope and y-intercept. Step 4: Plot the given point and use the slope in step 2 to locate another point to the line. Draw the line between these two points. �� ������������������������ ������������������ Graph the line that satisfies each condition. 4a. Graph the line 3x + y = -3 and the line that is parallel to it that passes through the point (1, 5). 4b. Graph the line y = 2 3 x + 2 and the line perpendicular to it that passes through (-2, 1). Solutions 4a. The slope of 3x + y = -3 is found by writing the equation in slope-intercept form. 3x + y = -3 3x + y - 3x = -3 - 3x y = -3x - 3 The slope of the given line is m = -3. So, the slope of a line parallel to it is also m = -3 since parallel lines have the same slope. Graph the given equation, y = -3x - 3, by plotting the y-intercept (0, -3) and then moving down 3 units vertically and right 1 unit horizontally to (1, -6). Graph the line parallel to y = -3x - 3 and through (1, 5), by plotting (1, 5). From this point, move down 3 units vertically and right 1 unit horizontally to (2, 2). 4 2 (1, 5) (2, 2) –4 –2 2 4 (0, –3) (1, –6) –4 x y 3x + y = –3 4b. The line y = 2 3 x + 2 has slope m = 2 3 . The line perpendicular to it has slope m=- 3 2 since perpendicular lines have slopes that are negative reciprocals. Graph the line, y = 2 3 x + 2, by plotting the y-intercept (0, 2) and then rising 2 units vertically and moving right 3 units horizontally to get to (3, 4). Objective 4 ▶ Graph parallel or perpendicular lines if given the equation of one line and a point on the line parallel or perpendicular to it.
hendricks_beginning_algebra_1e_ch1_3
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