Question

Identify an equation in point-slope form for the ine parallel to y = -2/3 x+8 that

passes through (4, -5).
A. y+5= 3/2(x-4)
B. y-5= -2/3 (x+4)
C. y+5= -2/3(x-4)
D. y-4= 2/3(x+5)

help please 15points!!

Answer 1

`y +5 = -(2)/(3)(x - 4)`

Explanation:

Given

`y = -(2)/(3)x + 8`

Point (4,-5)

Required

Determine the line equation

From the question, we understand that the line is parallel to
`y = -(2)/(3)x + 8`

This implies that they have the same slope, m

A linear equation is:

`y = mx + b`

Where

`m = slope`

By comparison:
`y = mx + b` and
`y = -(2)/(3)x + 8`

`m = -(2)/(3)`

Next, we determine the line equation using:

`y - y_1 = m(x - x_1)`

Where

`(x_1,y_1) = (4,-5)` and
`m = -(2)/(3)`

`y - (-5) = -(2)/(3)(x - 4)`

`y +5 = -(2)/(3)(x - 4)`

Hence,

Option C is correct