Answer:
[tex]y=-\frac{4}{3} x+\frac{10}{3}[/tex]
Step-by-step explanation:
First, we need to get this in y=mx+b form.
m=slope
b=y axis intercept
8x+6y+1=0
8x+6y=-1
6y=-8x-1
[tex]y=-\frac{4}{3}x-\frac{1}{6}[/tex]
now that we have it in y=mx+b form, we know the slope. For the new equation, the slope will be the same and the only thing we don't know is the y axis intercept, so we'll have to solve for it.
[tex]6=-\frac{4}{3}(-2)+b\\6=\frac{8}{3} +b\\\frac{10}{3}=b[/tex]
Now that we know b, we just put it with the rest of the equation.
[tex]y=-\frac{4}{3} x+\frac{10}{3}[/tex]