Question

The line y=−x+1
is drawn on the coordinate plane. It is translated 1 unit to the right and 2 units up. What is the equation of the translated line?(1 point)
Responses

y=x+3
y equals x plus 3

y=x+4
y equals x plus 4

y=3
y equals 3

y=−x+4

Answer 1

To find the equation of the translated line, we need to start with the original equation and apply the translation.

The original line is given by the equation:

\[ y = -x + 1 \]

**Step 1: Translate 1 unit to the right.**

To translate the line 1 unit to the right, we replace \( x \) with \( x - 1 \) in the equation:

\[ y = - (x - 1) + 1 \]

This simplifies to:

\[ y = -x + 1 + 1 = -x + 2 \]

**Step 2: Translate 2 units up.**

Now, to translate the line 2 units up, we add 2 to the entire equation:

\[ y = -x + 2 + 2 = -x + 4 \]

So the equation of the translated line is:

\[ y = -x + 4 \]

Thus, the answer is:

**y = −x + 4**