The equation provided is $y = -x + 2$, which has a slope of $-1$ and a y-intercept of $2$.

Steps to find the correct graph:

1. Y-Intercept: The graph should cross the y-axis at $y = 2$.
2. Slope: Since the slope is $-1$, the line will decrease by $1$ unit on the y-axis for every $1$ unit increase on the x-axis, creating a downward diagonal line from left to right.

Identifying the Correct Option

• Look for the graph with a line that intercepts the y-axis at $2$ and has a negative slope, moving downward as it goes from left to right.
• Based on these characteristics, Option C is the correct answer, as it matches the line $y = -x + 2$.

Would you like more details on the concept of slopes and intercepts?

Here are some related questions to deepen your understanding:

1. How does the slope affect the orientation of a line on a graph?
2. What happens to the graph of $y = -x + 2$ if the slope changes to $1$?
3. How would the graph look if the y-intercept was changed to $-2$ instead of $2$?
4. Can you identify the line equation if only the graph is given without any labels?
5. How do positive and negative slopes visually differ on a graph?

Tip: To quickly identify the slope and intercept in an equation, remember that in the form $y = mx + b$, $m$ is the slope, and $b$ is the y-intercept.