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Over [174]
2 years ago
8

Determine the equation of the line that is perpendicular to the given line, through the given point.

Mathematics
1 answer:
exis [7]2 years ago
4 0

Answer:

The equation of the line is y + 7 = -\frac{1}{3}(x - 9)

Step-by-step explanation:

Equation of a line:

The equation of line, in point-slope form, is given by:

y - y_0 = m(x - x_0)

In which m is the slope and the point is (x_0, y_0)

Perpendicular lines:

If two lines are perpendicular, the multiplication of their slopes is -1.

Through (9,-7)

This means that x_0 = 9, y_0 = -7

So

y - y_0 = m(x - x_0)

y - (-7) = m(x - 9)

y + 7 = m(x - 9)

Perpendicular to y = 3x + 4

This line has slope 3, so:

3m = -1

m = -\frac{1}{3}

Thus

y + 7 = m(x - 9)

y + 7 = -\frac{1}{3}(x - 9)

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