Find the slope intercept form of the line passing thru the pt (4,-3) and parallel to the line 5x+8y=-3

Question

I don’t need final answer; please show how to solve it. Thanks in advance.

Answer 1

Slope intercept form of line equation is y = mx + b. m = slope and b = y -intercept.
Rewrite the equation in slope intercept form 
5x+8y=-3
subtract 5x from each side
5x+8y -5x=-5x-3
8y = -5x -3
divide each side by 8
y = -5/8 x - 3/8
slope = -5/8
the lines are parallel. so the slopes are same
the parallel line equation is y = -5/8x + b
substitute (4, -3) in the equation to get the b value.
-3 = -5/8 * 4 + b
b = -3 + 5/2 = -1/2
the parallel line equation is y = -5/8x -1/2