Question

What is the equation in point-slope form of a line that passes through the points (3, −5) and (−8, 4)?

A. y−4=−1/5(x+8)
B. y+4=−9/11(x−8)
C. y−4=−9/11(x+8)
D. y+4=−1/5(x−8)

Answer 1

C. y−4=−9/11(x+8)

that's your answer
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Answer 2

C.
`y-4=-(9)/(11)(x+8)`

Explanation:

The point slope form is
`y-y_1=m(x-x_1)` where m is the slope,

First we are going to calculate
`m`:

If you have two points:

`A=(x_1,y_1)\\B=(x_2,y_2)`

`m=(y_2-y_1)/(x_2-x_1)`

In this case: A=(-8,4) and B=(3,-5)

`x_1=-8, y_1=4\\x_2=3, y_2=-5`

Replacing in the formula:

`m=(-5-4)/(3-(-8))=-(9)/(11)`

Then
`y-y_1=-(9)/(11)(x-x_1)`,

Now we have to replace with:
`x_1=-8, y_1=4`,

`y-y_1=-(9)/(11)(x-x_1)\\\\y-4=-(9)/(11)(x-(-8))\\\\y-4=-(9)/(11)(x+8)`

Then the equation in point-slope form of a line that passes through the points (3, −5) and (−8, 4) is:

C.
`y-4=-(9)/(11)(x+8)`