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)%0D%0AResponses%0D%0A%0D%0Ay=5x+3%0D%0Ay equals 5 x plus 3%0D%0A%0D%0Ay=4x+2%0D%0Ay equals 4 x plus 2%0D%0A%0D%0Ay=3x−1%0D%0Ay equals 3 x minus 1%0D%0A%0D%0Ay=3x+1

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. Translation to the right: When we translate a line to the right by \( h \) units, we replace \( x \) with \( x - h \). In this case, \( h = 1 \), so we replace \( x \) with \( x - 1 \).

   The equation becomes: \[ y = 3(x - 1) + 2 \] Simplifying this gives: \[ y = 3x - 3 + 2 = 3x - 1 \]

2. Translation up: Now, we need to translate the line up by \( k = 2 \) units. This means we add \( k \) to \( y \): \[ y = 3x - 1 + 2 \] Simplifying gives: \[ y = 3x + 1 \]

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