What is the equation of the line that is perpendicular to $2 y = - 6 x + 8$ $2y=-6x+8$ if its $y$ $y$ -intercept is $5$ $5$ ?

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Answer 1 · 2016-07-26T09:49:36

$y = \frac{1}{3} x + 5$ $y=1/3x+5$

Given -

$2 y = - 6 x + 8$ $2y=-6x+8$

$y = \frac{- 6}{2} x + \frac{8}{2}$ $y=(-6)/2 x+8/2$
$y = - 3 x + 4$ $y=-3x+4$

The slope of this line is $m_{1} = - 3$ $m_1=-3$

Another line is passing through $(0, 5)$ $(0, 5)$
This line is perpendicular to the line $y = - 3 x + 4$ $y=-3x+4$

Find the slope of the other line -

$m_{2}$ $m_2$ is the slope of the other line.

For two lines to be perpendicular -

$m_{1} \times m_{2} = - 1$ $m_1 xx m_2 = -1$

Then

$m_{2} = \frac{- 1}{- 3} = \frac{1}{3}$ $m_2=(-1)/(-3)=1/3$

The equation is

$y = m x + c$ $y=mx+c$
$y = \frac{1}{3} x + 5$ $y=1/3x+5$

Look at the diagram

What is the equation of the line that is perpendicular to 2y=-6x+82y=−6x+82y=-6x+8 if its yyy-intercept is 555?