Question

What is the equation of the line passing through `(-5,4)` and has a slope of `m=-3/2`?

Answer 1

`y=(-3/2)x-7/2`

Explanation:

The equation of a straight line of slope `color(blue)m` and pasiing through point `(color(blue)(x_0,y_0))` is

`color(blue)(y-y_0=m(x-x_0))`

in this exercise given`m=-3/2` and passing through`(-5,4)`
Equation is:

`color(blue)(y-y_0=m(x-x_0))`
`rArry-4=-3/2(x-(-5))`
`rArry-4=-3/2(x+5)`
`rArry-4=(-3/2)x-15/2`
`rArry=(-3/2)x-15/2+4`

`rArry=(-3/2)x-15/2+8/2`
`rArry=(-3/2)x-7/2`