University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

465

Pages:

3
Author:

ignorantkd77o

Equations of Parallel and Perpendicular Lines (Day 2) Essential Question How can you write an equation of a line that is parallel or perpendicular to a given line and passes through a given point? 1 EXPLORATION: Writing Equations of Parallel and Perpendicular Lines Work with a partner. Write an equation of the line that is parallel or perpendicular to the given line and passes through the given point. Use a graphing calculator to verify your answer. What is the relationship between the slopes? a. Parallel (0,2) y = mx + b 2 = 3/2(0) + b 2 = 0 + b 2 = b So y = 3/2x + 2 coordinate plane with a line passing through (0,2) and the equation y = 3/2x 1 b. Perpendicular (0,1) y = mx + b 1 = -2/3(0) + b 1 = 0 + b 1 = b So y = -2/3x + 1 coordinate plane with a line passing through (0,1) and the equation y = 3/2x 1 c. Parallel (2, -2) y = mx + b -2 = 1/2(2) + b -2 = 1 + b -3 = b So y = 1/2x - 3 coordinate plane with a line passing through (2, 2) and the equation y = 1/2x + 2 d. Perpendicular (2, -3) y = mx + b -3 = -2(2) + b -3 = -4 + b 1 = b So y = -2x + 1 coordinate plane with a line passing through (2, 3) and the equation y = 1/2x + 2 e. Parallel (0, -2) y = mx + b -2 = -2(0) + b -2 = 0 + b -2 = b So y = -2x - 2 coordinate plane with a line passing through (0, 2) and the equation y = 2x + 2 f. Perpendicular (4, 0) y = mx + b 0 = 1/2(4) + b 0 = 2 + b -2 = b So y = 1/2x - 2 coordinate plane with a line passing through (4, 0) and the equation y = 2x + 2 EXPLORATION: Writing Equations of Parallel and Perpendicular Lines Go to BigideasMath.com for an interactive tool to investigate this exploration. Work with a partner. Write the equations of the parallel or perpendicular lines. Use (y = mx + b) a.Parallel to (y = 2x - 2) (y = 2x + 10) (y = 2x + 11) (y = 2x + 14) coordinate plane with two parallel lines b.Perpendicular to (y = 2x - 2) Відкриється в новому вікні flexbooks.ck12.org coordinate plane with two perpendicular lines Communicate Your Answer How can you write an equation of a line that is parallel or perpendicular to a given line and passes through a given point? Parallel: (y = \frac{2}{3}x + 7) (y = \frac{2}{3}x + b) (2, 1) = (x, y) (2) = \frac{2}{3}(6) + b keep going Perpendicular: (y = -\frac{3}{2}x + b) (2, 1) = (x, y) (2) = -\frac{3}{2}(6) + b keep going Write an equation of the line that is (a) parallel and (b) perpendicular to the line (y = 3x + 2) and passes through the point (1, -2) Parallel: (y = 3x + b) (-2) = 3(1) + b -2 = 3 + b -5 = b (y = 3x - 5) Perpendicular: