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WRITE EQUATIONS OF PARALLEL AND PERPENDICULAR LINES November 20, 2008 Pages 319-321

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SOLUTION 1.Write an equation of the line that passes through (–3,–5) and is parallel to the line y = 3x – 1. STEP 1 Identify the slope. The graph of the given equation has a slope of 3. So, the parallel line through (– 3, – 5) has a slope of 3.

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y = mx + by = mx + b – 5 = 3(– 3) + b 4 = b Write slope-intercept form. Substitute 3 for m, 3 for x, and 25 for y. Solve for b. STEP 3 Write an equation. Use y = mx + b. y = 3x + 4 Substitute 3 for m and 4 for b. STEP 2 Find the y- intercept. Use the slope and the given point.

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SOLUTION 2. Determine which lines, if any, are parallel or perpendicular. Line a: y = 5x – 3 Line b: x +5y = 2 Line c: –10y – 2x = 0 Find the slopes of the lines. Line a: The equation is in slope-intercept form. The slope is 5.

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Line b: x + 5y = 2 5y = – x + 2 Line c: – 10y – 2x = 0 – 10y = 2x y = – x 1 5 x 2 5 1 5 + – Write the equations for lines b and c in slope- intercept form.

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ANSWER Lines b and c have slopes of –, so they are parallel. Line a has a slope of 5, the negative reciprocal of –, so it is perpendicular to lines b and c. 1 5 1 5

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Assignment: Pages 322-3244 - 26 even 28, 38, 39

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