#### Transcript Chapter 5-6: Geometry -Parallel and Perendicular Lines

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 The line parallel to Replace m with point-slope form. has the same slope, and (x, y) with (4, -2) in the Point-slope form Replace m with y with –2, and x with 4. Simplify. Distributive Property Subtract 2 from each side. Write the equation in slopeintercept form. Answer: The equation is Check You 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: 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. Find the slope of each segment. Slope of Slope of Slope of Answer: The slope of of and is 1 and the slope is not perpendicular to and , so it cannot be used to measure height. The graph shows the diagonals of a rectangle. Determine whether is perpendicular to Answer: The slope of is Since is and the slope of is not perpendicular to Write the slope-intercept form for an equation of a line that passes through (4, –1) and is perpendicular to the graph of Step 1 Find the slope of the given line. Original equation Subtract 7x from each side. Simplify. Divide each side by –2. Simplify. Step 2 The slope of the given line is So, the slope of the line perpendicular to this line is the opposite reciprocal of or Step 3 Use the point-slope form to find the equation. Point-slope form and Simplify. Distributive Property Subtract 1 from each side. Simplify. Answer: The equation of the line is Check You can check your result by graphing both equations on a graphing calculator. Use the CALC menu to verify that passes through (4, –1). Write the slope-intercept form for an equation of a line that passes through (–3, 6) and is perpendicular to the graph of Answer: Write the slope-intercept form for an equation of a line perpendicular to the graph of and passes through (0, 6). Step 1 Find the slope of Original equation Subtract 5x from each side. Simplify. Divide each side by 2. Simplify. Step 2 The slope of the given line is So, the slope of the line perpendicular to this line is the opposite reciprocal of or Step 3 Substitute 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 x1 with 0, y1 with 6, and m with Distributive Property Answer: The equation of the line is 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: