Explanation:
to be parallel it has to have the same slope as the other line.
to be able to see the slope directly in the equation, we need to transform it into the slope-intercept form :
y = ax + b
"a" being the slope, "b" being the y-intercept (the y- value when x = 0).
4x + 3y = 3
3y = -4x + 3
y = (-4/3)x + 3/3 = (-4/3)x + 1
the slope is -4/3. for the original line, and also for our desired line, which has to have the same slope, as mentioned.
"b" for our desired line we get by using the given point coordinates in the half-finished equation :
0 = (-4/3)×-3 + b = 4 + b
b = -4
and our equation is
y = (-4/3)x - 4