Question

What is the equation of the line that passes through `(3, —3)` and a slope of 3?

Answer 1

Use the gradient and one point equation and rearrange into the form `y=mx+c`

Explanation:

The equation of a line can be found if the gradient or 'slope' and one point on the line is know can be found with the equation: `y-y_1 = m(x-x_1)` when you have the coordinates `(x_1,y_1)` and the gradient `m`.

Substituing in the values for your case we get: `y-(-3) = 3(x-3)`

Cleanining up the two negatives and expanding the brackets on the right hand side we get: `y+3 = 3x-9`

Now we take away 3 from both sides to get it in the form `y=mx+c`

This results in the equation and answer to your question: `y = 3x-6`