Question

write the equation of this line in slope - intercept form.
write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0, -5)\) (the y - intercept) and \((8, -2)\).

Step2: Calculate the slope (\(m\))

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0, - 5)\) and \((x_2,y_2)=(8, - 2)\). Then \(m=\frac{-2-(-5)}{8 - 0}=\frac{-2 + 5}{8}=\frac{3}{8}\).

Step3: Write the slope - intercept form

The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We know that \(m = \frac{3}{8}\) and \(b=-5\) (since the line crosses the y - axis at \((0,-5)\)). So the equation of the line is \(y=\frac{3}{8}x-5\).

Answer:

\(y = \frac{3}{8}x-5\)