graph the line with slope -2 and y - intercept -4.

Explanation:

Step1: Write the equation of the line

The slope - intercept form of a line is (y = mx + b), where (m) is the slope and (b) is the (y) - intercept. Given (m=-2) and (b = - 4), the equation is (y=-2x - 4).

Step2: Plot the (y) - intercept

The (y) - intercept is ((0,-4)). So, we first plot the point ((0,-4)) on the coordinate plane.

Step3: Use the slope to find another point

The slope (m=-2=\frac{\Delta y}{\Delta x}=\frac{-2}{1}). From the point ((0,-4)), if we move (1) unit to the right (increase (x) by (1)) and (2) units down (decrease (y) by (2)), we get the point ((1,-6)).

Step4: Draw the line

Connect the points ((0,-4)) and ((1,-6)) and extend the line in both directions.

Answer:

The line with equation (y = - 2x-4) is graphed by first plotting the (y) - intercept ((0,-4)) and then using the slope (-2) (rise (-2), run (1)) to find another point ((1,-6)) and connecting them.