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

Answer 1

To find the equation of the new line after Lucy translates her original line \( y = 3x + 2 \) one unit to the right and two units up, we can follow these steps:

1. **Translation to the Right**:
Translating the line one unit to the right involves replacing \( x \) with \( x - 1 \).
Substitute \( x - 1 \) into the original equation:
\[
y = 3(x - 1) + 2 = 3x - 3 + 2 = 3x - 1
\]

2. **Translation Up**:
Now, we need to translate the resulting line \( y = 3x - 1 \) two units up. This means we add 2 to the \( y \)-value:
\[
y = 3x - 1 + 2 = 3x + 1
\]

So the equation of the new line after the transformations is:
\[
y = 3x + 1
\]

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