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:

$y=-3x-7$