Answer:
[tex]y=-\frac{6}{7} x-\frac{74}{7}[/tex]
Step-by-step explanation:
First we put our equation into slope intercept form by subtracting 6x from both sides and then dividing by 7.
6x + 7y = 13 --> [tex]y=-\frac{6}{7}+\frac{13}{7}[/tex]
The line is parallel which means they both have the same slope.
[tex]y=-\frac{6}{7} +b[/tex]
Now we need to find b. this is where the given point comes in. We can find b by substituting -3 for x and -8 for y.
[tex]-8=-\frac{6}{7} (-3)+b[/tex]
Then we multiply and give the numbers a common denominator so it is easier to manipulate. Remember that a negative times a negative is a positive.
[tex]-\frac{56}{7} =\frac{18}{7} +b[/tex]
Now we subtract [tex]\frac{18}{7}[/tex] from both sides so that the equation equals b
[tex]\frac{-74}{7}=b[/tex]
Finally we but b back into the equation [tex]y=-\frac{6}{7} +b[/tex]
[tex]y=-\frac{6}{7} x-\frac{74}{7}[/tex]
