Question

Write a function rule of a line in slope intercept form that is parallel to line 5x - 3y = 7 and has the same y intercept of the line 4x-y=9

Answer 1

y =
`(5)/(3)` x -9

Explanation:

Put both equations in the slope intercept form

y =mx + b

5x - 3y = 7 Subtract 5x from both sides

-3y = -5x + 7 Divide both sides by -3

y =
`(-5)/(-3)` x +
`(7)/(-3)` Cleaned up

y =
`(5)/(3)` x -
`(7)/(3)`

4x -y = 9 Subtract 4x from both sides

-y = -4x + 9 Divide all the way through by -1

y = 4x - 9

To make a line parallel to the first equation, we need the same slope. The slope of the first equation is
`(5)/(3)`. We are also told to have the same y intercept as the second equation which is -9

y =
`(5)/(3)` x - 9