determine the equation of the line. (type an equation. simplify your answer. type your answer in slope…

Answer:

(y = \frac{4}{3}x - 2)

Explanation:

Step1: Find two points on the line

From the graph, two points are ((0,- 2)) and ((3,2)).

Step2: Calculate the slope (m)

The slope formula is (m=\frac{y_2 - y_1}{x_2 - x_1}). Let ((x_1,y_1)=(0,-2)) and ((x_2,y_2)=(3,2)). Then (m=\frac{2-(-2)}{3 - 0}=\frac{4}{3}).

Step3: Use the slope - intercept form (y=mx + b)

We know (m = \frac{4}{3}) and from the point ((0,-2)), (b=-2) (since when (x = 0), (y=b) in (y=mx + b)). Substitute (m) and (b) into the formula: (y=\frac{4}{3}x-2).