Question

The graph of the line 4x+3y= 12 is translated right 1 unit and down 3 units. What is the equation of the new line?

Answer 1

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.