Question

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

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((-8, -1)\) and \((0, -7)\). The point \((0, -7)\) is the y - intercept (\(b\)) since when \(x = 0\), \(y=-7\).

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

The formula for slope between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(-8,-1)\) and \((x_2,y_2)=(0,-7)\).

$$m=\frac{-7-(-1)}{0 - (-8)}=\frac{-7 + 1}{8}=\frac{-6}{8}=-\frac{3}{4}$$

Step3: Write the equation in 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 found that \(m =-\frac{3}{4}\) and \(b=-7\). So the equation of the line is \(y =-\frac{3}{4}x-7\).

Answer:

\(y =-\frac{3}{4}x - 7\)