Question

What is the equation of the line that goes through `(3, -6)` and is parallel to the line `3x+y-10=0`?

Answer 1

`y+6=-3(x-3)`

Explanation:

Let us find the slope of the given line `3x+y-10=0`.

By subtracting 3x from and adding 10 to both sides,

`Rightarrow y=-3x+10`

So, the slope is `-3`.

To find an equation of the line, we need two pieces of information:

1. A point on the line: `(x_1, y_1)=(3,-6)`
2. The slope: `m=-3` (same as the given line)

By Point-Slope Form `y-y_1=m(x-x_1)`,

`y+6=-3(x-3)`

This can be simplified to give

Slope -intercept form: `" "y = -3x+3`

Or standard form: `" "3x+y =3`

I hope that this was clear.