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?

4 answers

To shift the line one unit to the right, we need to subtract 1 from the x-coordinate. To shift it two units up, we need to add 2 to the y-coordinate.

Therefore, the new line will have the equation y = 3(x-1) + 2.

Simplifying this equation, we get y = 3x - 1.

Therefore, the equation of the new line is y = 3x - 1.
A point is translated on the coordinate plane from (4,−1)
to (4,2)
. Journey writes the function g(y)=y+k
to describe the translation. What is the value of k?
To find the value of k, we need to determine the amount of vertical shift that occurred during the translation.

The original point (4, -1) was translated to the new point (4, 2). We can see that the y-coordinate changed from -1 to 2, which is an increase of 3 units.

Since the function g(y) = y + k represents a vertical shift, the value of k is equal to the amount of vertical shift. In this case, k = 3.

Therefore, the value of k is 3.
im doning the unit 4 lesson 16 10th grade transformations unit test Connexus
Jarvis wants to translate rectangle ABDC
horizontally by −4 and vertically by +3 to produce rectangle A′B′D′C′. What will be the coordinates of C′ after Jarvis completes this translation?