determine the equation, in slope - intercept form, for the line shown in the graph below:

Explanation:

Step1: Find two points on the line

Let's take two points (-24,18) and (24, - 18).

Step2: Calculate the slope (m)

The slope formula is (m=\frac{y_2 - y_1}{x_2 - x_1}). Substituting the points: (m=\frac{-18 - 18}{24-(-24)}=\frac{-36}{48}=-\frac{3}{4}).

Step3: Find the y - intercept (b)

We use the slope - intercept form (y = mx + b) and substitute one of the points, say ((0,y)) (when (x = 0)). Using the point ((-24,18)) and (m=-\frac{3}{4}) in (y=mx + b), we get (18=-\frac{3}{4}\times(-24)+b). Simplifying the right - hand side: (18 = 18 + b), so (b = 0).

Step4: Write the equation

The slope - intercept form is (y=mx + b). Substituting (m =-\frac{3}{4}) and (b = 0), we get (y=-\frac{3}{4}x).

Answer:

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