WRITE EQUATIONS OF PARALLEL AND

PERPENDICULAR LINESNovember 20, 2008

Pages 319-321

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.

y = 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 2Find the y-intercept. Use the slope and the given point.

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.

Line b: x + 5y = 2

5y = – x + 2

Line c: – 10y – 2x = 0

– 10y = 2x

y = – x15

xy =25

15 +

–

Write the equations for lines b and c in slope-intercept form.

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.

15

15

Assignment:

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