graph the line with the equation ( y = -\frac{1}{4}x - 7 ).

Explanation:

Step1: Identify the y - intercept

The equation is in slope - intercept form (y = mx + b), where (b) is the y - intercept. For (y=-\frac{1}{4}x - 7), (b=-7). So, plot the point ((0,-7)).

Step2: Identify the slope

The slope (m =-\frac{1}{4}). From the point ((0,-7)), use the slope to find another point. Since (m=\frac{\text{rise}}{\text{run}}=-\frac{1}{4}), from ((0,-7)), move down 1 unit (rise = - 1) and right 4 units (run = 4) to get the point ((4,-8)).

Step3: Draw the line

Connect the points ((0,-7)) and ((4,-8)) with a straight line.

Answer:

Plot the y - intercept ((0,-7)), use the slope (m =-\frac{1}{4}) to find another point ((4,-8)) and draw a straight line through these two points.