Lesson 4 3 TopicObjective To write the equation

Lesson 4. 3 Topic/Objective: To write the equation of a line in slope-intercept form that is parallel or perpendicular to a given line and passes through a specific point. EQ: How do you write parallel and perpendicular equations? Two nonvertical lines are parallel if and only if they have the same slope.

EXAMPLE Write the equation of the line that is parallel to the line y = 2 x + 5 and passes through the point (-2, 6). m=2 1. Identify the slope (m) from the equation. EXAMPLE 2. Identify the x and y from the coordinate (ordered pair). x = -2 y =6 3. Substitute into y= mx +b and solve for b. 6 = 2(-2) + b 6=-4 +b +4 + 4 10 = b 4. Write the equation. y = 2 x +10

EXAMPLE Write the equation of a line parallel to y = -5 x – 3 and passes through the point (- 4, -7). 1. Identify the slope (m). m = -5 2. Identify the x and y from the coordinate. x=-4 y = -7 3. Substitute into y = mx + b and solve for b. -7 = -5(-4) + b -7 = 20 + b -20 -27 = b 4. Write the equation. y = -5 x - 27

Two different nonvertical lines are perpendicular if and only if their slopes are opposite reciprocals of each other. Negative Reciprocal Examples Number Negative Reciprocal 3 -2

EXAMPLE Write the equation of a line perpendicular to the line y = -2 x + 2 and passing through (6, 8). m = -2. Perpendicular slope = ½. Replace ½ into y =mx +b then find b Use (6, 8) for (x, y) 8 = ½(6) + b 8=3+b -3 -3 5=b The equation of the perpendicular line is y = ½ x + 5.

EXAMPLE Try this. Find the equation of a line perpendicular to the equation y = -1/3 x – 2 and through the point (-2, -3). m=3 y = mx + b -3 = 3(-2) + b -3 = -6 + b 6 6 3=b y = 3 x + 3