# Line n passes through points (6,5) and (0, 1). What is the y-intercept of line k, if line k is perpendicular to line n and passes through the point (2,4)?

Dec 8, 2017

7 is the y-intercept of line k

#### Explanation:

First, let's find the slope for line n.
$\frac{1 - 5}{0 - 6}$
$\frac{- 4}{-} 6$
$\frac{2}{3} = m$
The slope of line n is 2/3. That means the slope of line k, which is perpendicular to line n, is the negative reciprocal of 2/3, or -3/2. So the equation we have so far is:
$y = \left(- \frac{3}{2}\right) x + b$
To calculate b or the y-intercept, just plug in (2,4) into the equation.
$4 = \left(- \frac{3}{2}\right) \left(2\right) + b$
$4 = - 3 + b$
$7 = b$
So the y-intercept is 7