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

Answer:

To graph the line (y = - 2x+2), we can use the slope - intercept form (y = mx + b), where (m=-2) (slope) and (b = 2) (y - intercept).

Explanation:

Step1: Plot the y - intercept

The y - intercept is (b = 2). So, we plot the point ((0,2)) on the y - axis.

Step2: Use the slope to find another point

The slope (m=-2=\frac{\Delta y}{\Delta x}). From the point ((0,2)), we move (1) unit to the right (since (\Delta x = 1)) and (2) units down (since (\Delta y=-2)). This gives us the point ((1,0)).

Step3: Draw the line

Connect the points ((0,2)) and ((1,0)) with a straight line. Extend the line in both directions.

So, the line (y=-2x + 2) passes through the points ((0,2)) and ((1,0)) and has a slope of (-2).