Slope of Parallel and Perpendicular LinesGeometry 17.0 – Students prove theorems by using coordinate geometry, including various forms of equations of lines.

Find the Slope of a line parallel

Find the Slope of a line perpendicular

Step 1: To find the slope of the line, rewrite the equation in slope-intercept form.6x – 3y = 9 –3y = –6x + 9 Subtract 6x from each side. y = 2x – 3 Divide each side by –3.

The line 6x – 3y = 9 has slope 2.Step 2: Use point-slope form to write an equation for the new line.

y – y1 = m(x – x1) y – (–8) = 2(x – (–5)) Substitute 2 for m and (–5, –8) for (x1, y1). y + 8 = 2(x + 5) Simplify.

Step 1: To find the slope of the given line, rewrite the equation in slope-intercept form. 5x + 2y = 1

2y = –5x + 1 Subtract 5x from each side.

y = – x + Divide each side by 2.52

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Step 2: Find the slope of a line perpendicular to 5x + 2y = 1. Let m be the slope of the perpendicular line.

Step 3: Use point-slope form, y – y1 = m(x – x1), to write an equation for the new line.