Question

A given line has the equation 2x + 12y = −1.

What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (0, 9)?

y = (
)x + 9

Answer 1

Answer:

y = 6x + 9

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 2x + 12y = - 1 into this form

Subtract 2x from both sides

12y = - 2x - 1 ( divide all terms by 12 )

y = - $\frac{1}{6}$ x - $\frac{1}{12}$ ← in slope- intercept form

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

Given a line with slope m then the slope of a line perpendicular to it is

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

Note the line crosses the y- axis at (0, 9) → c = 9

y = 6x + 9 ← equation of line