Question

Find the equation of the line with Slope = −3-3 and passing through (2,−13)(2,-13) . Write your equation in the form y=mx+by=mx+b .

Answer 1

Given that the slope of the line is:

`m=-3`

And knowing that the line passes through this point:

`\mleft(2,-13\mright)`

You need to remember that the Slope-Intercept Form of the equation of a line is:

`y=mx+b`

Where "m" is the slope of the line and "b" is the y-intercept.

In order to find the value of "b", you can substitute the slope and the coordinates of the point on the line, into the equation:

`-13=(-3)(2)+b`

Now you can solve for "b":

`\begin{gathered} -13=-6+b \\ -13+6=b \\ b=-7 \end{gathered}`

Knowing "m" and "b", you can write the following equation of the line in Slope-Intercept Form:

`y=-3x-7`

Hence, the answer is:

`y=-3x-7`