Question

How do i solve this i do not get it.... Find the equation of the line that contains the point left parenthesis negative 3 comma negative 9 right parenthesis and is parallel to the line 3 x plus 4 y equals 7. Write the equation in​ slope-intercept form, if possible.

Answer 1

`y = -(3)/(4)x - (45)/(4)`

Explanation:

When ever you are asked to draw a line that goes through a given point you should use point slope formula or
`y - y_(1) =m(x - x_(1))`. In this problem you are asked to go through point (-3, -9) while being parallel to 3x+4y = 7.

1. Start by converting 3x+4y = 7 into slope intercept form (y = mx + b). To do this you first need to move 3x to the other side of the equation: 4y = -3x + 7. Then divide by 4 to get y alone:
   `y = -(3)/(4) x + (7)/(4)`.
2. Next, start plugging the numbers into the point slope formula given above, where
   `y_(1)` is -9,
   `x_(1)` is -3, and
   `m` is
   `-(3)/(4)`. Your equation should look like this when you're done:
   `y - (-9) = -(3)/(4)(x - (-3))`.
3. When you subtract a negative you add so your equation becomes:
   `y + 9 = -(3)/(4)(x+3)`.
4. You then need to distribute the
   `-(3)/(4)` into the
   `(x+3)` and you should end up with something like this:
   `y+9 = -(3)/(4)x - (9)/(4)`
5. Finally, subtract the 9 from the left side and you have your answer:
   `y = -(3)/(4)x - (45)/(4)`