Question

Lucy draws a line with the equation y=3x+2 . She translates the line by shifting it one unit to the right and two units up. Which is the equation of the new line?

A. y = 5x + 3
B. y = 3x + 1
C. y = 4x + 2
D. y = 3x - 1

Answer 1

To translate the line given by the equation \(y = 3x + 2\) one unit to the right and two units up, we need to adjust the equation accordingly.

**Step 1: Shift the line one unit to the right.**
- To shift a line one unit to the right, we replace \(x\) with \(x - 1\).
- The equation becomes:
\[
y = 3(x - 1) + 2
\]
- Simplifying this:
\[
y = 3x - 3 + 2
\]
\[
y = 3x - 1
\]

**Step 2: Shift the line two units up.**
- To shift the line two units up, we add 2 to the entire equation. So we take the current equation \(y = 3x - 1\) and add 2:
\[
y = 3x - 1 + 2
\]
\[
y = 3x + 1
\]

The final equation after translating the line is:
\[
y = 3x + 1
\]

Thus, the correct answer is **B. y = 3x + 1**.