Question

write an equation of the line below.

Explanation:

Step1: Identify two points on the line

From the graph, we can see two points: \((0, -3)\) (the y - intercept) and \((-6, -7)\).

Step2: Calculate the slope \(m\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0, - 3)\) and \((x_2,y_2)=(-6, -7)\). Then \(m=\frac{-7-(-3)}{-6 - 0}=\frac{-7 + 3}{-6}=\frac{-4}{-6}=\frac{2}{3}\).

Step3: Use the slope - intercept form \(y=mx + b\)

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 \(m=\frac{2}{3}\) and from the point \((0,-3)\), the y - intercept \(b=-3\). So the equation of the line is \(y=\frac{2}{3}x-3\).

Answer:

\(y = \frac{2}{3}x-3\)