Question

Find the equation of the line that contains the point (-3,-8) and is parallel to the line 6x + 7y = 13. Write the equation in slope-intercer Select the correct choice below and fill in the answer box to complete your choice. (Use integers or fractions for any numbers in the equation.) l​

Answer 1

`y=-(6)/(7) x-(74)/(7)`

Explanation:

First we put our equation into slope intercept form by subtracting 6x from both sides and then dividing by 7.

6x + 7y = 13 -->
`y=-(6)/(7)+(13)/(7)`

The line is parallel which means they both have the same slope.

`y=-(6)/(7) +b`

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.

`-8=-(6)/(7) (-3)+b`

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.

`-(56)/(7) =(18)/(7) +b`

Now we subtract
`(18)/(7)` from both sides so that the equation equals b

`(-74)/(7)=b`

Finally we but b back into the equation
`y=-(6)/(7) +b`

`y=-(6)/(7) x-(74)/(7)`