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 equals 3 x minus 1
y=5x+3
y equals 5 x plus 3
y=3x+1
y equals 3 x plus 1
y=4x+2
y equals 4 x plus 2
To translate the line one unit to the right and two units up, we need to make the following changes to the original equation:
- Increase the x-coordinate by 1
- Increase the y-coordinate by 2
So, the equation of the new line is obtained by substituting these changes into the original equation:
Original equation: y = 3x + 2
New equation: y = 3(x+1) + 2
Simplifying, we get: y = 3x + 3 + 2
Combining like terms, the equation of the new line is:
y = 3x + 5
Thus, the correct answer is:
y = 3x + 5
To shift the line one unit to the right and two units up, you need to adjust the equation y = 3x + 2.
To shift one unit to the right, you need to subtract 1 from the x-value. This means replacing x with x - 1.
To shift two units up, you need to add 2 to the y-value. This means replacing y with y + 2.
So the equation of the new line after the translation is y = 3(x - 1) + 2.
Now we can simplify the equation:
y = 3(x - 1) + 2
y = 3x - 3 + 2
y = 3x - 1
Therefore, the equation of the new line after the translation is y = 3x - 1.