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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) Responses

y=3x+1 y=3x-1 y=5x+3 y=4x+2

1 answer

To shift the line given by the equation \( y = 3x + 2 \) one unit to the right and two units up, we can perform the following transformations:

  1. Shift one unit to the right: To shift the graph of a function \( f(x) \) to the right, we replace \( x \) with \( (x - 1) \). For the equation \( y = 3x + 2 \), this gives us: \[ y = 3(x - 1) + 2 = 3x - 3 + 2 = 3x - 1 \]

  2. Shift two units up: To shift the graph of a function up by \( c \) units, we add \( c \) to the entire function. In this case, we will add 2 to the equation we got from the first step: \[ y = (3x - 1) + 2 = 3x + 1 \]

Thus, the equation of the new line after the transformations is: \[ y = 3x + 1 \]

So the correct response is:

  • y=3x+1