Geometry: Chapter and 3.7: Writing equations for Parallel and Perpendicular Lines

Postulate 17: Slopes of Parallel Lines In a coordinate plane, two nonvertical lines are parallel if and only if they have the same slope. Any two vertical lines are parallel. The equation for the slope of a line is:

Linear equations may be written in different forms. The general form of the linear equation in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. The y-intercept is the value of y when x=0.

Postulate 18: Slopes of Perpendicular Lines In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is -1. If the slope of one line is 2, the perpendicular slope of the other lines is -½. The two slopes are negative reciprocals.

Ex. 3: Write an equation of a line perpendicular to y = -½x – 1 that passes through the point (3, -4).

m = 2 -4 = 2(3) + b -4 = 6 + b -10= b y = 2x -10 You can check that the lines are perpendicular by graphing the lines and measuring the angle with a protractor.

Ex. 4 The graph shows the cost of having cable television installed in your home. Write an equation of the line. Explain the meaning of the slope and the y-intercept of the line. Image taken from: Geometry. McDougal Littell: Boston, P. 182.

Ex. 4 The graph has points at (0, 80) and (1, 120). m = 40 and b = 80 y =40x + 80 The slope is the cost per month, and the y- intercept is the initial charge.

Ex. 5 Graph a line with equation in standard form. Graph: 2x – 3y = -12.

Ex. 5 (cont.) Step 1—Find the intercepts. To find the x-intercept, let y = 0. 2x – 3(0) = -12 2x = -12 x = -6 To find the y-intercept, let x = 0. 2(0) – 3y = -12 – 3y = -12 y = 4 Step 2—Graph the line. The graph intersects the axes at (0,4) and (-6, 0). Graph these points, then draw a line through the points. Image taken from: Geometry. McDougal Littell: Boston, P. 182.