Question

The line y= -x +1 is drawn on the coordinate plane. It is translated 2 unit to the right and 2 units up. What is the equation of the translated line? Hint: Try graphing (1 point) Responses y = -x + 4 y = -x + 4 y = x + 3 y = x + 3 y = -x + 5 y = -x + 5 y = 3

Answer 1

To find the equation of the translated line, we first start with the original line equation:

\[ y = -x + 1. \]

Now, we will translate this line 2 units to the right and 2 units up.

1. **Translation to the right (2 units):**
- When we translate a graph to the right, we replace \(x\) with \(x - a\) where \(a\) is the number of units we move to the right. Here, \(a = 2\).
- So, we replace \(x\) in the original equation:
\[ y = - (x - 2) + 1. \]
This simplifies to:
\[ y = -x + 2 + 1 = -x + 3. \]

2. **Translation upwards (2 units):**
- When moving the graph up by \(b\) units, we add \(b\) to the equation. Here, \(b = 2\).
- Adding 2 to our equation:
\[ y = -x + 3 + 2 = -x + 5. \]

Thus, the equation of the translated line is:

\[
\boxed{y = -x + 5}.
\]