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)
0 y =5x +3
Оу =3х -1
0y =3x+1
0 y=4x+2

Answer 1

To find the equation of the line after translating it, we start with the original line equation:

\[ y = 3x + 2 \]

**Step 1:** Shift the line 1 unit to the right.
When we shift a line to the right by \(h\) units, we replace \(x\) with \(x - h\) in the equation.

For a shift of 1 unit to the right:
\[ y = 3(x - 1) + 2 \]
\[ y = 3x - 3 + 2 \]
\[ y = 3x - 1 \]

**Step 2:** Shift the line 2 units up.
When we shift a line up by \(k\) units, we add \(k\) to the entire equation.

For a shift of 2 units up:
\[ y = 3x - 1 + 2 \]
\[ y = 3x + 1 \]

Thus, the equation of the new line after translating 1 unit to the right and 2 units up is:

\[ y = 3x + 1 \]

Among the provided options, the correct choice is:

**\(y = 3x + 1\)**.