Lucy draws a line with the equation y = 3x + 2 She translates the fine by shifting it one unit to the right and two units up. Which is the equation of the new line? (1 point) y = 3x - 1; y = 5z + 3; y = 4x + 2; y = 3x + 1
The translation of the line one unit to the right can be achieved by replacing x with (x - 1) in the equation y = 3x + 2. This gives us y = 3(x - 1) + 2, which simplifies to y = 3x - 1 after distributive property.
Similarly, the translation of the line two units up is achieved by adding 2 to the equation obtained from the previous step. Therefore, the equation of the new line is y = 3x - 1 + 2.
Simplifying this equation gives us y = 3x + 1.
Therefore, the correct equation of the new line after the translation is y = 3x + 1.
To shift the line one unit to the right, we need to decrease the x-coordinate of each point on the line by 1. This is done by replacing x with (x-1) in the equation.
Similarly, to shift the line two units up, we need to increase the y-coordinate of each point on the line by 2. This is done by replacing y with (y+2) in the equation.
Therefore, the new equation of the line is:
y = 3(x-1) + 2
Simplifying this equation, we get:
y = 3x - 3 + 2
y = 3x - 1
So, the equation of the new line is y = 3x - 1.
To find the equation of the new line, which is obtained by translating the original line one unit to the right and two units up, we need to modify the equation of the original line.
Let's start with the original equation: y = 3x + 2.
To shift the line one unit to the right, we need to replace x with (x - 1) because subtracting 1 from x will shift the line one unit to the right. So, the equation becomes: y = 3(x - 1) + 2.
Now, to shift the line two units up, we need to add 2 to the y-intercept (the constant term). By doing this, the equation becomes: y = 3(x - 1) + 2 + 2.
Simplifying the equation, we have: y = 3(x - 1) + 4.
Expanding the brackets, we get: y = 3x - 3 + 4.
Further simplifying, we have: y = 3x + 1.
Therefore, the equation of the new line, obtained by shifting the original line one unit to the right and two units up, is y = 3x + 1.
So, the correct option is y = 3x + 1.