1. 4-7B Perpendicular Lines Algebra 1 Glencoe McGraw-HillLinda Stamper

2. What is the reciprocal of 8? What is the opposite reciprocal of 8? In this lesson you will need to find and use opposite reciprocals.

3. Two lines in a coordinate plane are perpendicular if they intersect at right angles (90 degree angles). Horizontal and vertical lines are perpendicular to each other. x y

4. In a coordinate plane, two non vertical lines are perpendicular if and only if the product of their slopes is –1. x y Do you think these lines are perpendicular?

5. How to determine whether lines are perpendicular. 1. Write each line in slope-intercept form. 2. Multiply the slopes together. 3. If the product is –1, then the lines are perpendicular.

6. Write the equation of each line in the graph. Determine whether the lines are perpendicular. x y Green line y-intercept is 3 Blue line y-intercept is – 1 The lines are perpendicular! These are opposite reciprocals !

7. Example 1 Write the equation of each line in the graph. Determine whether the lines are perpendicular. x y Green line y-intercept is 3 Blue line y-intercept is – 4 The lines are not perpendicular!

8. Example 2 Write the equation of each line in the graph. Determine whether the lines are perpendicular. x y Green line y-intercept is 1 Blue line y-intercept is – 4 The lines are perpendicular!

9. Write the slope-intercept form of an equation for the line that passes through (-4,-3) and is perpendicular to the graph of 4x + y = 2. x y (-4,-3) Find the slope of the given line. Find the opposite reciprocal. Use slope-intercept or point-slope to write the equation.

10. Write the slope-intercept form of an equation for the line that passes through (-4,-3) and is perpendicular to the graph of 4x + y = 2. Find the slope of the given line. Find the opposite reciprocal. Use slope-intercept or point-slope to write the equation. (when no graph is given)

11. Example 3 Write the slope-intercept form of an equation for the line that passes through (-3,-2) and is perpendicular to the graph of x + 4y = 12. Example 4 Write the slope-intercept form of an equation for the line that passes through (4,7) and is perpendicular to the graph of -2x + 3y = -3. Example 5 Write the slope-intercept form of an equation for the line that passes through (4,-1) and is perpendicular to the graph of 7x - 2y = 3. Find slope of given line. Find the opposite reciprocal. Use slope-intercept or point-slope form to write the equation.

12. Example 3 Write the slope-intercept form of an equation for the line that passes through (-3,-2) and is perpendicular to the graph of x + 4y = 12. Find slope of given line. Find the opposite reciprocal. Use slope-intercept or point-slope form to write the equation.

13. Example 4 Write the slope-intercept form of an equation for the line that passes through (4,7) and is perpendicular to the graph of -2x + 3y = -3. Find slope of given line. Find the opposite reciprocal. Use slope-intercept or point-slope form to write the equation.

14. Example 5 Write the slope-intercept form of an equation for the line that passes through (4,-1) and is perpendicular to the graph of 7x - 2y = 3. Find slope of given line. Find the opposite reciprocal. Use slope-intercept or point-slope form to write the equation.

15. Write an equation in slope-intercept form for a line perpendicular to the graph of -3x + 2y = 6 that passes through the x-intercept of the line. What is the problem asking you to do? x y -3x+2y=6 Write equation for this line. (but no graph is given)

16. Write an equation in slope-intercept form for a line perpendicular to the graph of -3x + 2y = 6 that passes through the x-intercept of the line. Find slope of given line. Find the opposite reciprocal. Find the x-intercept of the given line. Use slope-intercept or point-slope form to write the equation. Coordinate of x- intercept is (-2,0).

17. Write an equation in slope-intercept form for a line perpendicular to the graph of -3x + 2y = 6 that passes through the x-intercept of the line. x y

18. Example 6 Write an equation in slope-intercept form for a line perpendicular to the graph of x + 3y = 6 that passes through the x-intercept of the line. Example 7 Write an equation in slope-intercept form for a line perpendicular to the graph of 3x + 2y = 8 that passes through the y-intercept of the line. Find slope of given line. Find the opposite reciprocal. Use slope-intercept or point-slope form to write the equation. Find the intercept of given line.

19. Example 6 Write an equation in slope-intercept form for a line perpendicular to the graph of x + 3y = 6 that passes through the x-intercept of the line. Find slope of given line. Find the opposite reciprocal. Find the x-intercept of the given line. Use slope-intercept or point-slope form to write the equation. Coordinate of x- intercept is (6,0).

20. Example 7 Write an equation in slope-intercept form for a line perpendicular to the graph of 3x + 2y = 8 that passes through the y-intercept of the line. Find slope of given line. Find the opposite reciprocal. Find the x-intercept of the given line. Use slope-intercept or point-slope form to write the equation. Coordinate of y- intercept is (0,4).

21. 4-A15 Pages 240-241 #18–25,28-30,36 and Skills Practice Wkbk. Page 30 #13-24. Review nightly for trimester 1 exam.