graph the line with the equation $y = -x + 2$.

Explanation:

Step1: Identify the y-intercept

The equation is in slope - intercept form (y = mx + b), where (b) is the y - intercept. For (y=-x + 2), (b = 2). So the line crosses the y - axis at the point ((0,2)).

Step2: Determine the slope

The slope (m) of the line (y=-x + 2) is (- 1) (since (y=-1x + 2)). The slope (m=\frac{\text{rise}}{\text{run}}=-1=\frac{-1}{1}) or (\frac{1}{-1}).

Step3: Find another point

Using the y - intercept ((0,2)) and the slope. If we use the slope (\frac{-1}{1}), from ((0,2)), we move down 1 unit and right 1 unit to get the point ((1,1)). If we use the slope (\frac{1}{-1}), from ((0,2)), we move up 1 unit and left 1 unit to get the point ((-1,3)).

Step4: Draw the line

Plot the points ((0,2)), ((1,1)) (or ((-1,3))) and draw a straight line through them.

(Note: Since the problem is about graphing, the final answer is the graph of the line (y=-x + 2) passing through ((0,2)) and other points determined by the slope, like ((1,1)) or ((-1,3)) etc.)

Answer:

The line (y = -x+2) is graphed by plotting the y - intercept ((0,2)) and using the slope (-1) to find another point (e.g., ((1,1)) or ((-1,3))) and then drawing a straight line through these points.