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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.

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

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

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).

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

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.

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

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.

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

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.

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

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

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

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).

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:

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.

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

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

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: