q. write the equation of the line in slope - intercept form.

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through the points ((0, -4)) (the y - intercept) and ((2, 0)).

Step2: Calculate the slope ((m))

The formula for slope between two points ((x_1,y_1)) and ((x_2,y_2)) is (m=\frac{y_2 - y_1}{x_2 - x_1}). Using the points ((0,-4)) and ((2,0)), we have (x_1 = 0,y_1=-4,x_2 = 2,y_2 = 0). (m=\frac{0-(-4)}{2 - 0}=\frac{4}{2}=2)

Step3: Determine the y - intercept ((b))

The slope - intercept form of a line is (y=mx + b), where (b) is the y - intercept. We know that the line crosses the y - axis at ((0,-4)), so (b=-4).

Step4: Write the equation in slope - intercept form

Substitute (m = 2) and (b=-4) into the slope - intercept form (y=mx + b). We get (y = 2x-4)

Answer:

(y = 2x-4)