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

Answer:

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

Step-by-step 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:

$-\frac{1}{6}m = -1$

$m = 6$

So

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

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

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

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

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

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