Question

Someone please help :')

Answer 1

C.
`y+4=-3(x-3)`

Explanation:

The point-slope format is a way to represent the equation of a line. It involves using a point on the line and relating it to the slope in such a way that one can find any point on the line using the equation. One is asked to find the equation of a line in point-slope form. The general format for the point-slope form of a line is the following;

`y-h=m(x-k)`

Where the point on the line that is being used is (
`h,k`). The parameter (
`m`) represents the slope or rate of change in the line. The slope is often referred to as the (
`(rise)/(run)`) and can be found using the following formula.

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

Where (
`x_1,y_1`) and (
`x_2,y_2`) are points on the line. As one can see the following points can be found on the line:

`(3,-4), (0, 5)`

Substitute these points into the slope formula and solve for the slope;

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

=
`((5)-(-4))/((0)-(3))`

=
`(5+4)/(0-3)\\`

=
`(9)/(-3)`

=
`-3`

Now substitute the slope into the given formula. As per the problem, one is supposed to use the point (
`3, -4`) in the formula.

`y-h=m(x-k)`

Substitute the slope;

`y-h=-3(x-k)`

Substitute the point;

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