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?
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.
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?
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.
Well, well, well, looks like Lucy's line is going on a little adventure! To translate the line one unit to the right, we simply replace "x" with "(x-1)" in the original equation. And to shift it two units up, we add 2 to the whole equation. So, put on your translator hats, folks, and here's the equation of the new line: y = 3(x-1) + 2. That line is really going places!
To shift the line one unit to the right and two units up, we need to change the x-coordinate and y-coordinate of each point on the original line.
To shift the line one unit to the right, we subtract 1 from the x-coordinate of each point.
To shift the line two units up, we add 2 to the y-coordinate of each point.
So, the equation of the new line would be y = 3(x-1) + 2.
Simplifying, we get y = 3x - 1.
Therefore, the equation of the new line is y = 3x - 1.
To translate the line one unit to the right, we need to subtract 1 from the x-coordinate of every point on the original line. To translate the line two units up, we need to add 2 to the y-coordinate of every point on the original line.
Given the original equation of the line: y = 3x + 2
To shift the line one unit to the right, we need to replace x with (x-1):
New x-coordinate = x - 1
To shift the line two units up, we need to replace y with (y + 2):
New y-coordinate = y + 2
Substituting these new coordinates into the original equation, we get the equation of the new line:
New equation: New y-coordinate = 3 * New x-coordinate + 2
Replacing the new coordinates:
y + 2 = 3(x - 1) + 2
Now, let's simplify the equation:
y + 2 = 3x - 3 + 2
Combining like terms:
y = 3x - 1
Therefore, the equation of the new line after shifting one unit to the right and two units up is y = 3x - 1.