Slope/Standard Form questions...?

Question

1. What is the standard form of the equation y=1/4x-3?

2. Find the slope and y-intercept of the line: 5x-3y=19

Answer 1

1)Given equation is y = 1/4x - 3

y = (x - 12)/4

4y = x - 12

x - 4y -12 = o

There it is in the form of standard form of equation Ax +By + c = o

Here A = 1 , B = -4 and C = -12

2)5x - 3y = 19

General form of slope intercept form of line is y = mx + c

5x - 3y = 19

-3y = -5x + 19

3y = 5x - 19

y = (5/3) x - 19/3

Here slope m = 5/3 and y-intercept = -19/3