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

The equation of the line is
`y + 7 = -(1)/(3)(x - 9)`

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 = -(1)/(3)`

Thus

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

`y + 7 = -(1)/(3)(x - 9)`