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: $$\boxed{{\displaystyle y=3x+1}}.$$