Question

lucy draws a line with the equation y = 3x + 2. She translates the line by shifting one unit to the right and two units up. which is the equation of the new line?

Answer 1

The original line has the equation given by \( y = 3x + 2 \).

To translate the line one unit to the right and two units up, we need to adjust the equation accordingly.

1. **Shifting one unit to the right**: When a line is translated one unit to the right, we replace \( x \) with \( x - 1 \). So the equation becomes:
\[
y = 3(x - 1) + 2 = 3x - 3 + 2 = 3x - 1.
\]

2. **Shifting two units up**: To shift the line two units up, we simply add 2 to the entire equation:
\[
y = 3x - 1 + 2 = 3x + 1.
\]

Thus, the equation of the new line after the translation is:
\[
\boxed{y = 3x + 1}.
\]