Question

write an equation in slope - intercept form of the line. (use integers or fractions for any numbers in the equation.)

Explanation:

Step1: Find two points on the line

Let's take two points \((- 8,3)\) and \((0,5)\) from the graph.

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting \(x_1=-8,y_1 = 3,x_2 = 0,y_2=5\) gives \(m=\frac{5 - 3}{0-(-8)}=\frac{2}{8}=\frac{1}{4}\).

Step3: Identify the y - intercept \(b\)

The y - intercept is the y - value when \(x = 0\). From the point \((0,5)\), \(b = 5\).

Step4: Write the equation in slope - intercept form

The slope - intercept form is \(y=mx + b\). Substituting \(m=\frac{1}{4}\) and \(b = 5\) gives \(y=\frac{1}{4}x+5\).

Answer:

\(y=\frac{1}{4}x + 5\)