Answer: y = 7/3 - (4/3)*x
Step-by-step explanation:
First, let's write our line in the notation:
y = f(x)
So we must isolate y in the equation:
4x + 3y = 12
3y = 12 - 4x
y = 12/3 - (4/3)*x = 4 - (4/3)*x
Now, we have two translations, one horizontal and one vertical.
Let's define them in general cases:
Horizontal translation.
When we have y = f(x) and we want to do a horizontal translation of A units to the right (A positive) we have:
y = g(x) = f(x - A)
So we replace our variable x by x - A.
Vertical translation.
When we have y = f(x) and we want to do a horizontal translation of A units up (A positive) we have:
y = g(x) = f(x) + A.
Then in this case we have:
y = f(x) = 4 - (4/3)*x
then, the horizontal translation of 1 unit to the right is:
y = f(x - 1) = 4 - (4/3)*(x - 1)
And the translation of 3 units down (a vertical translation) is:
y = f(x - 1) - 3 = 4 - (4/3)*(x - 1) - 3 = 1 + 4/3 - (4/3)*x
y = 7/3 - (4/3)*x
This equation represents the new line.
