Question

Line c has an equation of y=-1/6x+5. Perpendicular to line c is line d, which passes through the point (-3,-8). What is the equation of line d

Answer 1

The equation of line d is
`y + 8 = 6(x + 3)`

Explanation:

Equation of a line:

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

`y - y_0 = m(x - x_0)`

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

Perpendicular lines:

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

Perpendicular to y=-1/6x+5

Slope of - 1/6, so:

`-(1)/(6)m = -1`

`m = 6`

So

`y - y_0 = 6(x - x_0)`

Passes through the point (-3,-8).

This means that
`x_0 = -3, y_0 = -8`. So

`y - y_0 = 6(x - x_0)`

`y - (-8) = 6(x - (-3))`

`y + 8 = 6(x + 3)`