Question

The graph of 2x + 3y = 12 is shifted down 3 units. What is the equation of the shifted graph? please explain

Answer 1

2x+3y=9
the slope will be he same, but the y intercept will be 3 down, thus 12 - 3 =9

Answer 2

The equation of a line is y=mx+b Where slope is m and b is the y intercept. In order to find what our equation needs to be we must first convert it into linear form (y=mx+b).

We have
2x+3y=12
we want y=mx+b

Using algebra:
2x+3y=12
3y=12-2x subtract 2x from both sides
y=12/3 - (2x)/3 divide both sides by 3
y=4-2x/3
y=-2x/3+4 rewritten

Which is what we want.
m=-2/3
b=4

b is the location on the y axis so if we move the location of our intercept down by 3, we have 4-3=1=b

Thus our final equation is
y=-2x/3+1