Question

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?

Answer 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?

Answer 2

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?

Answer 3

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.

Answer 4

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.