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)?

Answer 1

Answer:

$y=6x+9$

Step-by-step explanation:

Given equation of the line,

$2x + 12y = -1$

$12y=-2x-1$

$y=-\frac{1}{6}x-\frac{1}{12}$

Slope intercept form of a line is y = mx + c,

Where, m is the slope of the line,

By comparing, the slope of the given line is $\frac{-1}{6}$,

Since, when two lines are perpendicular then the product of their slope is -1,

Let $m_1$ be the slope of the perpendicular line of the given line,

$m_1\times -\frac{1}{6}=-1$

$\implies m_1=6$

Now, point slope intercept form of a line is,

$y_y_1=m(x-x_1)$

Where, $(x_1, y_1)$ is the point on the line,

Hence, the equation of the line passes through the point (0, 9) and having slope 6 is,

$y-9=6(x-0)$

$y-9=6x$

$y=6x+9$

Answer 2

Answer:

y = 6x + 9

Step-by-step explanation:

The equation of a line in slope- interceot 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 passes through (0, 9) on the y- axis ⇒ c = 9

y = 6x + 9 ← equation of perpendicular line