Question

What is the equation of the line that passes through `(-3,4)` and `(-1, -2)`?

Answer 1

`y + 3x + 5 = 0`

Explanation:

`color(red)(x_1->-3)`
`color(red)(x_2->-1)`
`color(red)(y_1->4)`
`color(red)(y_2->-2)`

The equation of a line is equal to:-

`color(green)[y-y_1=(y_1 - y_2)/(x_1-x_2) xx (x-x_1)]`

Put the above values in this equation.

You get

`color(brown)[y-4 = (4-(-2))/(-3-(-1)) xx [x-(-3)]]`

`color(brown)[=> y-4 = (4+2)/(-3+1) xx (x+3)]`

`color(purple)[=> y-4 = 6/-2 xx (x+3)]`

`color(purple)[=> y-4 = -3 xx (x+3)]`

`color(blue)[=> y-4 = -3x -9]`

`color(blue)[=> y + 3x -4 + 9 = 0]`

`color(orange)[=> y + 3x + 5 = 0]`