Question

which is the graph of $y = -x + 2$? (with four graphs labeled a, b, c, d and four answer options c, b, a, d)

Explanation:

Step1: Analyze the slope and y-intercept

The equation is \( y = -x + 2 \). In the slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, the slope \( m=- 1 \) (negative, so the line should be decreasing from left to right) and the y - intercept \( b = 2 \) (the line crosses the y - axis at \( (0,2) \)).

Step2: Analyze each graph

• For graph A: Check the slope and y - intercept. The line in graph A has a negative slope and seems to cross the y - axis at \( (0,2) \).
• For graph B: The slope is positive (increasing from left to right), so it can't be the graph of \( y=-x + 2 \) since our slope is negative.
• For graph C: The slope is positive (increasing from left to right), so it can't be the graph of \( y=-x + 2 \) since our slope is negative.
• For graph D: The y - intercept does not seem to be at \( (0,2) \), so it is not the correct graph.

Answer:

A