Question

Find an equation for the line parallel to 3x+5y-4=0, with the same x-intercept as 2x-3y-6=0.

Answer 1

It is 4y = -3x + 9

Explanation:

`3x + 5y - 4 = 0 \\ 5y = - 3x + 4 \\ y = - (3)/(4) x + 4`

since it is parallel, its slope, m is -¾

`2x - 3y - 6 = 0 \\ - 3y = - 2x + 6 \\ y = (2)/(3) x - 2`

at x-intercept, y is zero

`2 = (2)/(3) x \\ x = 3`

therefore

`y = mx + c \\ 0 = ( - (3)/(4) * 3) + c \\ c = (9)/(4)`

equation is

`y = - (3)/(4) x + (9)/(4) \\ \\ 4y = - 3x + 9`