Question

A) Lucy draws a line with the equation . 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 = 3x + 2
y = 5x + 3
y = 3x − 1
y = 3x + 1
y = 4x + 2

Answer 1

To find the new equation of the line after translating it one unit to the right and two units up, we need to apply these transformations to the original equation of the line.

1. **Translation one unit to the right:** This means replacing \( x \) with \( x - 1 \).
2. **Translation two units up:** This means adding 2 to the entire equation.

Starting with the original equation \( y = 3x + 2 \):

1. Replace \( x \) with \( x - 1 \):
\[
y = 3(x - 1) + 2
\]
\[
y = 3x - 3 + 2
\]
\[
y = 3x - 1
\]

2. Now, translate it two units up:
\[
y = 3x - 1 + 2
\]
\[
y = 3x + 1
\]

Thus, the equation of the new line after the translation is:

\[
\boxed{y = 3x + 1}
\]