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What is the equation of the line that passes through the point (7,-6)and has a slope of -2

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5 votes

Answer:

The equation of the required line is: 2x + y = 8

Explanation:

When a point on the line and the slope of the line are given, we use the slope - one - point form to determine the equation of the line.

Say,
$ (x_1, y_1) $ is the point passing through the line and the slope of the line is say,
m. Then the equation would be:


$ (y - y_1) = m(x - x_1) $

Here
$ (x_1, y_1) = (7, -6) $ and slope,
$ m = - 2 $.

Therefore, the equation of the line becomes:


$ y - (-6) = -2(x - 7) $


$ \implies y + 6 = -2x + 14 $

Rearranging we get:


$ 2x + y - 8 = 0 $ which is the required equation of the line.

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