graph the line with slope -3 passing through the point (-2, -3).

Explanation:

Step1: Use the point - slope form

The point - slope form of a line is (y - y_1=m(x - x_1)), where (m) is the slope and ((x_1,y_1)) is a point on the line. Given (m=-3), (x_1 = - 2), (y_1=-3), we have (y+3=-3(x + 2)).

Step2: Simplify the equation

Expand the right - hand side: (y+3=-3x-6). Then subtract 3 from both sides to get the slope - intercept form (y=-3x - 9).

Step3: Find another point

Let (x = 0), then (y=-3\times0-9=-9). So another point on the line is ((0,-9)).

Step4: Plot the points and draw the line

Plot the points ((-2,-3)) and ((0,-9)) on the coordinate plane. Then draw a straight line passing through these two points.

Answer:

Plot the point ((-2,-3)). Since the slope (m=-3=\frac{\Delta y}{\Delta x}), from the point ((-2,-3)), move 1 unit to the right (increase (x) by 1) and 3 units down (decrease (y) by 3) to get another point ((-1,-6)). Or use the (y) - intercept form (y=-3x - 9) (when (x = 0), (y=-9)) to plot the points ((-2,-3)) and ((0,-9)) and draw a straight line through them.