Given the graph of a line y=−x. Write an equation of a line which is perpendicular and goes through the point (8,2).

When a line is perpendicular to another line, the slope is the negative reciprocal of the other line's slope. So in this case, the slope would be 1, since the negative reciprocal of -1 is 1/1 which is 1.

To find the y-intercept, you have to substitute the point (8,2) into y = mx + b

2 = 1(8) + b

b = -6

The equation is y = x - 6

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abidemiokin abidemiokin · Answer 2 · 2021-09-24T15:18:54+02:00

The equation of the line which is perpendicular and goes through the point (8,2) is y = x - 6

The equation of the required line in slope-intercept form is expressed as:

y-y0 = m(x-x0) where:

m is the slope
(x0, y0) is the point on the line

Given the equation of the line as y = -x

Get the slope of the line

mx = -x

m = -1

Since the required line is perpendicular to this line, the required slope will be 1 (M = -(-1/1))

Get the required equation

Recall that;

y-y0 = m(x-x0)

y - 2 = 1(x-8)

y - 2 = x - 8

y = x - 8 + 2

y = x - 6

Hence the equation of the line which is perpendicular and goes through the point (8,2) is y = x - 6.

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