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Which pair of lines are perpendicular?

Select one:

a.
5x - y = 3 and 5x - y = 6


b.
5x - y = 6 and 2x + 10y = 22


c.
x - y = 1 and 2x - 2y = 2


d.
None of the these.

User NevenHuynh
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1 Answer

3 votes

Answer:

b. 5x - y = 6 and 2x + 10y = 22

Explanation:

When two lines are perpendicular, their slopes are negative reciprocals as shown by the following formula:

m2 = -1 / m1, where

  • m2 is the slope of one line,
  • and m1 is the slope of the other line.

Currently, 5x - y = 6 and 2x + 10y = 22 are in standard form whose general equation is:

Ax + By = C.

In order to determine the slopes of both lines, we can convert both lines to slope-intercept form, whose general equation is:

y = mx + b, where

  • m is the slope,
  • and b is the y-intercept.

Converting 5x - y = 6 to slope-intercept form:

(5x - y = 6) - 5x

(-y = -5x + 6) / -1

y = 5x - 6

Thus, the slope of 5x - y = 6 is 5.

Converting 2x + 10y = 22 to slope-intercept form:

(2x + 10y = 22) - 2x

(10y = -2x + 22) / 10

y = -1/5x + 11/5

Thus, the slope of 2x + 10y = 22 is -1/5.

Checking that the slopes are negative reciprocal:

To check that the slopes are negative reciprocals by plugging in both 5 and -1/5 for m1 in the perpendicular slope formula and checking that we get 5 and -1/5 respectively:

Checking 5 for m1:

m2 = -1 / 5

m2 = -1/5

Checking -1/5 for m1:

m2 = -1 / (-1/5)

m2 = -1 * -5/1

m2 = 5

Thus, the two slopes are negative reciprocals, and thus 5x - y = 6 and 2x + 10y = 22 are perpendicular.

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