Question

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

y=3x+4; (9, -7)​

Answer 1

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

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

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