graph $y = -3x + 7$.

Explanation:

Step1: Find the y - intercept

The equation is in slope - intercept form (y = mx + b), where (b) is the y - intercept. For (y=-3x + 7), when (x = 0), (y=7). So the point ((0,7)) is on the line.

Step2: Find the x - intercept

Set (y = 0). Then (0=-3x + 7). Solving for (x): [ \begin{align*} 3x&=7\ x&=\frac{7}{3}\approx2.33 \end{align*} ] So the point ((\frac{7}{3},0)) is on the line.

Step3: Use the slope to find another point

The slope (m=-3=\frac{\Delta y}{\Delta x}). From the y - intercept ((0,7)), if (\Delta x = 1), then (\Delta y=-3). So another point is ((0 + 1,7-3)=(1,4))

Plot the points ((0,7)), ((\frac{7}{3},0)), ((1,4)) and draw a straight line through them.

Answer:

Plot the points ((0,7)), ((\frac{7}{3},0)), ((1,4)) and draw a straight line through them to graph (y=-3x + 7).