1. Transparency 6 Click the mouse button or press the Space Bar to display the answers.

2. Example 6-1a Write the slope-intercept form of an equation for the line that passes through (4, –2) and is parallel to the graph of The line parallel tohas the same slope, Replace m with and (x, y) with (4, -2) in the point-slope form.

3. Point-slope form Replace m with y with – 2, and x with 4. Simplify. Distributive Property Subtract 2 from each side.

4. Example 6-1c Write the equation in slope- intercept form. Answer:The equation is

5. Example 6-1d CheckYou can check your result by graphing both equations. The lines appear to be parallel. The graph of passes through (4, –2).

6. Write the slope-intercept form of an equation for the line that passes through (2, 3) and is parallel to the graph of Answer:

7. Example 6-2a Geometry The height of a trapezoid is measured on a segment that is perpendicular to a base. In trapezoid ARTP, and are bases. Can be used to measure the height of the trapezoid? Explain.

8. Example 6-2b Find the slope of each segment. Slope of

9. Example 6-2c Answer: The slope of and is 1 and the slope of is not perpendicular to and, so it cannot be used to measure height.

10. Example 6-2d The graph shows the diagonals of a rectangle. Determine whether is perpendicular to Answer: The slope of is and the slope of is Sinceis not perpendicular to

11. Example 6-3a Write the slope-intercept form for an equation of a line that passes through (4, –1) and is perpendicular to the graph of Step 1Find the slope of the given line. Original equation Subtract 7x from each side. Simplify.

12. Example 6-3b Divide each side by –2. Simplify.Step 2The slope of the given line isSo, the slope of the line perpendicular to this line is the opposite reciprocal ofor

13. Example 6-3c Step 3Use the point-slope form to find the equation. Point-slope form and Simplify. Distributive Property

14. Example 6-3d Subtract 1 from each side. Simplify. Answer: The equation of the line is

15. Example 6-3e CheckYou can check your result by graphing both equations on a graphing calculator. Use the CALC menu to verify that passes through (4, –1).

16. Example 6-3f Write the slope-intercept form for an equation of a line that passes through (–3, 6) and is perpendicular to the graph of Answer:

17. Example 6-4a Write the slope-intercept form for an equation of a line perpendicular to the graph of and passes through (0, 6). Step 1Find the slope of Original equation Subtract 5x from each side. Simplify.

18. Example 6-4b Divide each side by 2. Simplify.Step 2The slope of the given line isSo, the slope of the line perpendicular to this line is the opposite reciprocal ofor

19. Example 6-4c Step 3Substitute the slope and the given point into the point-slope form of a linear equation. Then write the equation in slope-intercept form. Point-slope form Replace x 1 with 0, y 1 with 6, and m with Distributive Property Answer: The equation of the line is

20. Example 6-4d Write the slope-intercept form for an equation of a line perpendicular to the graph of and passes through the x -intercept of that line. Answer: