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 plus 1

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

y=3x−1
y equals 3 x minus 1

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

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. **Shift one unit to the right:** To shift the graph of a function \( f(x) \) one unit to the right, we replace \( x \) with \( x-1 \). So, the new equation will become:
\[
y = 3(x - 1) + 2
\]
Simplifying this, we have:
\[
y = 3x - 3 + 2 = 3x - 1
\]

2. **Shift two units up:** Next, we need to shift the entire graph two units up. This means we add 2 to the entire equation:
\[
y = 3x - 1 + 2
\]
Simplifying this, we find:
\[
y = 3x + 1
\]

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

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