Find the equation, in y=mx+b of the following:

Question

The line perperndicular to 2x+5y-3=0 and with the same x-intercept as 2x+3y+6=0

Answer 1

A line perpendicular to 2x+5y-3=0 has the form
5x - 2y = c , notice their slopes are opposite reciprocals.

the x-intercept of 2x+3y+6 = 0 ....
let y = 0, 2x = -6, x = -3
so (-3,0) must lie on our new line 5x - 2y = c
-15 - 0 = c, so c = -15

new line: 5x - 2y = -15
or in the form you want:
-2y = -5x - 15
y = (5/2)x + 15/2