Question

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)?

Answer 1

7 is the y-intercept of line k

Explanation:

First, let's find the slope for line n.
`(1-5)/(0-6)`
`(-4)/-6`
`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=(-3/2)x+b`
To calculate b or the y-intercept, just plug in (2,4) into the equation.
`4=(-3/2)(2)+b`
`4=-3+b`
`7=b`
So the y-intercept is 7