Lucy draws a line with the equation y=3x +2. She translates the line by shifting it one to the right and two up. Which is the equation of the new line?
To shift the line one unit to the right, we need to subtract one from the x-coordinate. Therefore, the x-coordinate will change to x-1.
To shift the line two units up, we need to add two to the y-coordinate. Therefore, the y-coordinate will change to y+2.
So, the new equation of the line will be y+2 = 3(x-1).
To translate the line one unit to the right and two units up, we need to make the following changes to the equation:
1. Replace "x" with "x - 1" to shift the line one unit to the right.
2. Replace "y" with "y - 2" to shift the line two units up.
Therefore, the equation of the new line is:
y - 2 = 3(x - 1)
To translate the line, we need to adjust the equation by shifting it one unit to the right and two units up.
Shifting one unit to the right means we need to replace 'x' in the original equation with '(x - 1)', since when 'x' increases by 1, the line shifts one unit to the right.
So, the new equation, after shifting one unit to the right, would be: y = 3(x - 1) + 2.
Simplifying the equation: y = 3x - 3 + 2, which reduces to y = 3x - 1.
Now, we need to shift the line two units up. This means we add 2 to the constant term of the equation.
The final equation of the new line, after shifting one unit to the right and two units up, would be: y = 3x - 1 + 2.
Simplifying the equation: y = 3x + 1.
Therefore, the equation of the new line after the translation is y = 3x + 1.