Question

Write an equation that is parallel to y = 3x and passes through (-4 , -3)

Answer 1

The slopes of two parallel lines must be identical.

We have slope $m=3$, so the slope for the parallel line be the same.

Now, to find an equation that also passes through the given point, we use slope-point form, $y-y_1=m(x-x_1)$, where our point $(-4,-3)$ is substituted for $(x_1,y_1)$.

$y+3=3(x+4)$

Now, we convert to slope-intercept form as such.

$y=3x+12-3\\y=3x+9$

And we are done. :) We can verify graphically that these are indeed parallel lines. See attached.