Answer:
y=4x+23
Explanation:
Convert given equation into slope-intercept form:
12x-3y=10
4x-y=10/3
-y=10/3-4x
y=-10/3+4x
y=4x-10/3
Because the new equation must be parallel to the old equation, the slope stays the same, but the y-intercept changes based on the point that the new equation should pass through:
y=4x+b
3=4(-5)+b
3=-20+b
23=b
This means the slope-intercept form of the equation of the line that passes through (-5,3) and is parallel to 12x-3y=10 is y=4x+23