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Which equation represents a line that is perpendicular to Line L on the graph below?A. Y= -1/2x+3B. Y= 1/2x+3C. Y=2x+3D. Y= -2x+3

Which equation represents a line that is perpendicular to Line L on the graph below-example-1
User AMTourky
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1 Answer

2 votes

In this question, we are given a line. The standard equation of line is:

y = mx + b

Here, m is the slope, that is the difference of y values over the x values.

m = (y2 - y1) / (x2 - x1)

b is the y-intercept, where the value of x is zero.

If we see the line, x = 0, when y = -4. Hence, the y-intercept = b = -4

Also,

(x1, y1) = (0, -4)

(x2, y2) = (-4, 4)

m = [4 - (-4)]/ [-4 - 0]

m = 8/-4

m = -2

Hence, the equation of given line is

y = -2x - 4

The rule is: two lines are perpendicular if their slopes are negative reciprocal of each other.

In other words, two lines with slope m1 and m2 are perpendicular if

m1 = -1/m2

Now, the slope (m1) of the given line is -2. Hence, the slope (m2) of the perpendicular line would be m2 = 1/-(-2) = 1/2

Now, just put this value, we get

Y = 1/2 x - 4

As there is no solution closer to this one, I believe the 2nd answer Y = 1/2x + 3 would be correct.

User Keelan
by
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