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)
Responses

y=3x−1
y equals 3 x minus 1

y=5x+3
y equals 5 x plus 3

y=4x+2
y equals 4 x plus 2

y=3x+1

Answer 1

To find the new equation of the line after translating it one unit to the right and two units up, we can start with the original equation \(y = 3x + 2\).

1. **Shifting the line one unit to the right** involves replacing \(x\) with \(x - 1\):
\[
y = 3(x - 1) + 2
\]
Simplifying that:
\[
y = 3x - 3 + 2 = 3x - 1
\]

2. **Shifting the line two units up** involves adding 2 to the entire equation:
\[
y = (3x - 1) + 2
\]
Simplifying that:
\[
y = 3x + 1
\]

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

Therefore, the correct response is:
**y = 3x + 1**.