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Transparency 6. Click the mouse button or press the Space Bar to display the answers. Write the slope-intercept form of an equation for the line that passes through (4 , –2) and is parallel to the graph of.

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

  2. 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 to has the same slope, Replace m with and (x, y) with (4, -2) in the point-slope form. Example 6-1a

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

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

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

  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. Geometry The height of a trapezoid is measuredon a segment that isperpendicular to a base. In trapezoid ARTP, and arebases. Can be used tomeasure the height of the trapezoid?Explain. Example 6-2a

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

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

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

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

  12. Divide each sideby –2. Simplify. Step 2The slope of the given line is So, the slope of the line perpendicular to this line is the opposite reciprocal of or Example 6-3b

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

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

  15. Check You can check your result by graphing bothequations on a graphing calculator. Use theCALC menu to verify that passes through (4, –1). Example 6-3e

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

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

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

  19. Point-slope form Replace x1 with 0, y1 with 6, and m with Distributive Property Answer: The equation of the line is 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.

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

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