# How do you write an equation in point-slope form for the given y-intercept (0, 5) and is perpendicular to the line with equation y = –3x + 1?

##### 1 Answer
Aug 30, 2015

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

#### Explanation:

Given Line
Red line represents this line - y = -3 +1

Blue line is the required line. This line is vertical to y = -3 +1 and passing through the point (0, 5)

Since the two lines are vertical, the product of their slopes is equal to - 1

${m}_{1} \times {m}_{2} = - 1$
${m}_{1}$ is the slope of the given line(Red line)
${m}_{2}$ is the slope of the required line (blue)

$- 3 \times {m}_{2} = - 1$
${m}_{2} = \frac{- 1}{- 3} = \frac{1}{3}$

$y - {y}_{1} = {m}_{2} \left(x - {x}_{2}\right)$
$y - 5 = \frac{1}{3} \left(x - 0\right)$

The equation of the line is -
$y = \frac{1}{3} x + 5$