Question

Line 1 passes through (-3, 8) and (0, 4).

Answer 1

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

Step-by-step explanation:

Given

`(x_1,y_1)=(-3,8)`

`(x_2,y_2)=(0,4)`

Required

Determine the line equation

First, calculate the slope (m)

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

This gives:

`m = (4-8)/(0 - (-3))`

`m = (4-8)/(0 +3)`

`m = (-4)/(3)`

`m = -(4)/(3)`

The equation is then calculated using:

`y = m(x - x_2) + y_2`

Where

`m = -(4)/(3)` and
`(x_2,y_2)=(0,4)`

So, we have:

`y = -(4)/(3)(x-0) + 4`

`y = -(4)/(3)x+0 + 4`

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