Date Equations of Parallel and Perpendicular Lines

Warm up ✤ Graph the following two lines on the same coordinate plane. Then choose one word to describe the relationship between the two lines. ✤ y = 3x + 2 ✤ y = 3x - 1 ✤ Graph the following two lines on the same coordinate plane. Then choose one word to describe the relationship between the two lines. ✤ y = 1/2x - 4 ✤ y = -2x + 3

Slopes of Parallel & Perpendicular Lines ✤ Parallel lines: always have the same slope ✤ Perpendicular lines: always have opposite reciprocal slopes

Creating Parallel & Perpendicular Slopes ✤ Given the linear equation, state the slope of a parallel line and a perpendicular line. ✤ 1. y = 3x + 4 ✤ 2. y = -1/2x + 2 ✤ 3. y = -5x - 1

Forms of Linear Equations ✤ Slope-intercept form: y = mx + b where m = slope, b = y-intercept ✤ Point-slope form: y - y 1 = m(x - x 1 ) where m = slope and (x 1, y 1 ) is a point from the coordinate plane

Example of Point-Slope Form ✤ Given a slope and a point the line goes through, create the equation of the line. Put the equation into slope-intercept form. ✤ m = -2 and (-4, 3) ✤ y - 3 = -2(x - -4) ✤ y - 3 = -2(x + 4) ✤ y - 3 = -2x - 8 ✤ y = -2x - 5

Another Example ✤ Given a slope and a point the line goes through, determine the equation for the line. ✤ m = 1/2 and (6, -5) ✤ y - -5 = 1/2(x - 6) ✤ y + 5 = 1/2x - 6/2 ✤ y + 5 = 1/2x - 3 ✤ y = 1/2x - 8