heres a graph of a linear function. write the equation that describes that function. express it in slope…

Explanation:

Step1: Find two points on the line

Let's take two points ((x_1,y_1)=(- 4,2)) and ((x_2,y_2)=(4,4)) from the graph.

Step2: Calculate the slope (m)

The slope - formula is (m=\frac{y_2 - y_1}{x_2 - x_1}). Substituting the values, we get (m=\frac{4 - 2}{4-(-4)}=\frac{2}{8}=\frac{1}{4}).

Step3: Find the y - intercept (b)

We use the slope - intercept form (y = mx + b). Substitute (m=\frac{1}{4}) and the point ((x,y)=( - 4,2)) into the equation: (2=\frac{1}{4}\times(-4)+b). Then (2=-1 + b), so (b = 3).

Step4: Write the equation

The slope - intercept form of the line is (y=\frac{1}{4}x + 3).

Answer:

(y=\frac{1}{4}x + 3)