Parallel and Perpendicular Lines and Slopes Practice

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This worksheet is for 11th grade analytic geometry students. Find the requested slopes and line equations using the rules for parallel and perpendicular lines.

Find the slope of a line parallel to y = 7x - 4.
Find the slope of a line perpendicular to y = -(3/4)x + 2.
Find the slope of a line perpendicular to 3x - 6y = 12.
Write the equation of the line passing through (4, 1) that is parallel to y = -2x + 9.
Write the equation of the line passing through (-3, 2) that is perpendicular to y = 3x - 1 in slope-intercept form.
Find the equation of the perpendicular bisector of the line segment joining A(2, 4) and B(6, 8).

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Parallel and Perpendicular Lines and Slopes Practice

Answer key

Find the slope of a line parallel to y = 7x - 4.
m = 7
Find the slope of a line perpendicular to y = -(3/4)x + 2.
m = 4/3
Find the slope of a line perpendicular to 3x - 6y = 12.
Rewrite in slope-intercept form: y = (1/2)x - 2. The original slope is 1/2, so the perpendicular slope is -2.
Write the equation of the line passing through (4, 1) that is parallel to y = -2x + 9.
Using point-slope form: y - 1 = -2(x - 4), which simplifies to y = -2x + 9. Because it shares the same intercept, it is coincident; in standard form it is 2x + y = 9.
Write the equation of the line passing through (-3, 2) that is perpendicular to y = 3x - 1 in slope-intercept form.
The perpendicular slope is -1/3. Equation: y - 2 = -1/3(x + 3), which expands to y = -1/3 x + 1.
Find the equation of the perpendicular bisector of the line segment joining A(2, 4) and B(6, 8).
Midpoint is ((2+6)/2, (4+8)/2) = (4, 6). The slope of AB is (8 - 4)/(6 - 2) = 4/4 = 1. The perpendicular slope is -1. Equation: y - 6 = -1(x - 4), or y = -x + 10.