Question

write the equation of the line in slope-intercept form, $y = mx + b$.

Explanation:

Step1: Find the slope \(m\)

Use the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points on the line, say \((0,-3)\) and \((3,-1)\).
\(m=\frac{-1-(-3)}{3 - 0}=\frac{-1 + 3}{3}=\frac{2}{3}\)

Step2: Find the \(y\) - intercept \(b\)

The \(y\) - intercept \(b\) is the \(y\) - value when \(x = 0\). From the point \((0,-3)\), \(b=-3\)

Step3: Write the equation

Substitute \(m=\frac{2}{3}\) and \(b =- 3\) into \(y=mx + b\)
\(y=\frac{2}{3}x-3\)

Answer:

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