Question

A line contains the piont (4,5) and is perpendicular to a line with a slope of -2/3. Write an equarion of the line satisfying the given conditions. Write the answer in slope-intercept form

Answer 1

y =
`(3)/(2)` x - 1

Explanation:

Given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(2)/(3) )` =
`(3)/(2)` , then

y =
`(3)/(2)` + c ← partial equation in slope- intercept form

To find c substitute (4, 5) into the partial equation

5 = 6 + c ⇒ c = 5 - 6 = - 1

y =
`(3)/(2)` x - 1 ← equation of line

Answer 2

`y=(3)/(2)x-3.5` or, preferably,
`y=(3)/(2)x-(7)/(2)`

Explanation:

First is to find the perpendicular slope. In this case, you swap the numerator and denominator and then multiply that fraction by -1.

In this case, -2/3's inverse slope is 3/2.

Now, the initial y=3/2 passes through 7.5,5

So, you must subtract 3.5 from that to make it pass through 4,5.

In this way, you get the answer in slope-intercept form.