Warm Up Write an equation in slope-intercept form of the line having the given slope and passing through the given point. m = -3/2, (-8,9) M = ¼, (-8,6) y = -3/2 x – 3 y = ¼x + 8

News Wall Unit 4 quizzes (and corrections for half of your credit back) and tests must be completed by next Wednesday February 4th. We will be wrapping up unit 4 this Friday, January 30th.

Objectives Write equations to describe lines parallel or perpendicular to a given line.

Questions of the Day How do you write and equation of a line through a given point that is parallel or perpendicular to a given line?

Vocabulary parallel lines perpendicular lines

Review Parallel lines are lines in the same plane that have no points in common. In other words, they do not intersect. Parallel lines are lines have the same slope. Perpendicular lines are lines that intersect to form right angles (90°). In other words, two lines are perpendicular if the slopes have opposite signs and are reciprocals.

Example 4A: Geometry Application Show that ABC is a right triangle. If ABC is a right triangle, AB will be perpendicular to AC. slope of slope of AB is perpendicular to AC because Therefore, ABC is a right triangle because it contains a right angle.

If PQR is a right triangle, PQ will be perpendicular to PR. Check It Out! Example 4B Show that P(1, 4), Q(2,6), and R(7, 1) are the vertices of a right triangle. If PQR is a right triangle, PQ will be perpendicular to PR. P(1, 4) Q(2, 6) R(7, 1) slope of PQ slope of PR PQ is perpendicular to PR because the product of their slopes is –1. Therefore, PQR is a right triangle because it contains a right angle.

Example 5A: Writing Equations of Parallel and Perpendicular Lines Write an equation in slope-intercept form for the line that passes through (4, 10) and is parallel to the line described by y = 3x + 8. Step 1 Find the slope of the line. y = 3x + 8 The slope is 3. The parallel line also has a slope of 3. Step 2 Solve for the y-intercept (b), by substituting the slope and the point into the slope intercept form of the equation. y = mx + b Use the slope intercept form. Substitute 3 for m, 4 for x, and 10 for y. 10 = 3(4) + b

Example 5A Continued Write an equation in slope-intercept form for the line that passes through (4, 10) and is parallel to the line described by y = 3x + 8. Step 3 Write the equation in slope-intercept form. y = 3x – 2

Example 5B: Writing Equations of Parallel and Perpendicular Lines Write an equation in slope-intercept form for the line that passes through (2, –1) and is perpendicular to the line described by y = 2x – 5. Step 1 Find the slope of the line. y = 2x – 5 The slope is 2. The perpendicular line has a slope of because

Use the slope intercept form. Example 5B Continued Write an equation in slope-intercept form for the line that passes through (2, –1) and is perpendicular to the line described by y = 2x – 5. Step 2 Solve for the y-intercept (b), by substituting the slope and the point into the slope intercept form of the equation. y= m(x) + b Use the slope intercept form. Substitute for m, –1 for y, and 2 for x. -1= (2) + b Step 3 Write the equation in slope-intercept form.

Helpful Hint If you know the slope of a line, the slope of a perpendicular line will be the "opposite reciprocal.”

Check It Out! Example 5C Write an equation in slope-intercept form for the line that passes through (5, 7) and is parallel to the line described by y = x – 6. Step 1 Find the slope of the line. The slope is . y = x –6 The parallel line also has a slope of .

Check It Out! Example 5C Continued Write an equation in slope-intercept form for the line that passes through (5, 7) and is parallel to the line described by y = x – 6. Step 2 Solve for the y-intercept (b), by substituting the slope and the point into the slope intercept form of the equation. y = m(x) + b Use the slope intercept form. 7 = 4/5(5) + b Step 3 Write the equation in slope-intercept form.

Check It Out! Example 5D Write an equation in slope-intercept form for the line that passes through (–5, 3) and is perpendicular to the line described by y = 5x. Step 1 Find the slope of the line. y = 5x The slope is 5. The perpendicular line has a slope of because .

Check It Out! Example 5D Continued Write an equation in slope-intercept form for the line that passes through (–5, 3) and is perpendicular to the line described by y = 5x. Step 2 Solve for the y-intercept (b), by substituting the slope and the point into the slope intercept form of the equation. Use the point-slope form. y = m(x) + b 3 = -1/5(-5) + b Step 3 Write the equation in slope-intercept form.

Practice before the quiz Write an equation in slope-intercept form of the line that is parallel to the graph of each equation and passes through the given point. y = 3x - 5 1. y = 3x + 6; (4,7) 2. y = 1/2x + 5; (4,-5) y = 1/2x - 7 Write an equation in slope-intercept form of the line that is perpendicular to the graph of each equation and passes through the given point. 3. y = -5x + 1; (10,-1) y = 1/5x - 3 4. y = -4x - 2; (4,-4) y = 1/4x - 5

Lesson Quiz Write an equation is slope-intercept form for the line described. 1. contains the point (8, –12) and is parallel to 2. contains the point (4, –3) and is perpendicular to y = 4x + 5