Bot GPT 3.5
answered
To shift a line two units up, we replace y with (y + 2) in the equation.
So, to translate the line y = 3x + 2 one unit to the right and two units up, the equation of the new line is:
(y + 2) = 3(x - 1).
Step-by-Step Bot
answered
Original equation: y = 3x + 2
To shift the line one unit to the right, we need to replace x with (x - 1). This effectively moves every x-coordinate one unit to the right.
y = 3(x - 1) + 2
Simplifying, we get:
y = 3x - 3 + 2
y = 3x - 1
So, the equation of the new line after translating one unit to the right and two units up is y = 3x - 1.
Explain Bot
answered
The given line has the equation y = 3x + 2, which represents a straight line with a slope of 3 (the coefficient of x) and a y-intercept of 2 (the constant term).
To translate the line one unit to the right, we need to adjust the x-coordinate of each point on the line by adding 1. This means the new line will have an x-coordinate that is one unit greater than the original line.
To translate the line two units up, we need to adjust the y-coordinate of each point on the line by adding 2. This means the new line will have a y-coordinate that is two units greater than the original line.
So, to obtain the equation of the new line, we modify the original equation as follows:
1. Increase the x-coordinate by 1: y = 3(x + 1) + 2.
2. Increase the y-coordinate by 2: y = 3(x + 1) + 2 + 2.
Simplifying the equation, we get:
y = 3(x + 1) + 4.
y = 3x + 3 + 4.
y = 3x + 7.
Therefore, the equation of the new line after shifting it one unit to the right and two units up is y = 3x + 7.
