Give the equation of the line that is parallel to y=-3x+1 and goes through (-5,-6)

Hi there! The answer is y = -3x - 21

Let's set up the equation of the line step by step! First we need to know that we need to set up an equation in slope-intercept form. We get the following:

y = ax + b.
a represents the slope of the line.
b represents the intercept with the y-axis.

Since our new line is parallel to y = -3x + 1, both lines have the same slope. Therefore the slope of our line, which is represented by a, is -3.

y = -3x + b.
We also know that this line goes through the point (-5, -6) and therefore we can plug in these coordinates into our formula.

-6 = -3 × -5 + b
Simplify

-6 = 15 + b
Subtract 15

-21 = b
Switch sides

b = -21
Hence, y = -3x - 21

~ Hope this helps you!