Lucy draws a line with the equation y=3x+2

Question

𝑦
=
3
𝑥
+
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

y=4x+2
𝑦
=
4
𝑥
+
2
y equals 4 x plus 2

y=3x+1
𝑦
=
3
𝑥
+
1
y equals 3 x plus 1

y=3x−1
𝑦
=
3
𝑥
−
1
y equals 3 x minus 1

y=5x+3

Answer 1

To find the equation of the new line after translating the original line $y=3x+2$ one unit to the right and two units up, we can follow these steps:

1. Translating the line one unit to the right:

   • To shift a line $y=mx+b$ to the right by $h$ units, we replace $x$ with $x-h$. Here, $h=1$, so the new equation becomes:
     $$y=3(x-1)+2$$ $$y=3x-3+2$$ $$y=3x-1$$

2. Translating the line two units up:

   • To shift the line $y=mx+b$ up by $k$ units, we add $k$ to the entire equation. Here, $k=2$, so we add 2 to the last equation: $$y=3x-1+2$$ $$y=3x+1$$

Thus, the equation of the new line after the translation is $y=3x+1$.

Therefore, the correct response is: y = 3x + 1