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? (1 point)
• y = 32 + 1
• у = 4x + 2
0g=3-1
• y= 5г +3

Answer 1

To translate the line given by the equation \( y = 3x + 2 \) one unit to the right and two units up, we can follow these steps:

1. **Translating the line one unit to the right:** This will change the \( x \) in the equation. We replace \( x \) with \( x - 1 \):
\[
y = 3(x - 1) + 2
\]
Simplifying this:
\[
y = 3x - 3 + 2 = 3x - 1
\]

2. **Translating the line two units up:** We add 2 to the entire equation from the previous step:
\[
y = 3x - 1 + 2
\]
Simplifying this:
\[
y = 3x + 1
\]

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

Looking at the options, the closest match is not present. It seems the options may contain typographical errors or other mistakes. However, based on our calculations, the correct answer for the new line is \( y = 3x + 1 \).