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

Answer 1

To find the equation of the new line after translating the line given by the equation \(y = 3x + 2\) one unit to the right and two units up, we need to understand how translations affect the equation of the line.

1. Shifting a line one unit to the right means replacing \(x\) with \(x - 1\) in the equation.
2. Shifting the line two units up means adding 2 to the entire equation.

Starting with the original equation:
\[
y = 3x + 2
\]

**Step 1: Shift one unit to the right:**
Replace \(x\) with \(x - 1\):
\[
y = 3(x - 1) + 2
\]
\[
y = 3x - 3 + 2
\]
\[
y = 3x - 1
\]

**Step 2: Shift two units up:**
Now add 2 to the entire equation:
\[
y = 3x - 1 + 2
\]
\[
y = 3x + 1
\]

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

So the correct answer is \(A. y = 3x + 1\).