Question

write the equation of the line in fully simplified slope - intercept form.

Explanation:

Step1: Find the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points \((0,2)\) and \((5,-4)\).
\(m=\frac{-4 - 2}{5 - 0}=\frac{-6}{5}=-\frac{6}{5}\)

Step2: Use the slope - intercept form \(y = mx + b\)

We know \(b\) (the \(y\) - intercept) is \(2\) (from the point \((0,2)\)) and \(m =-\frac{6}{5}\)
Substitute \(m\) and \(b\) into \(y=mx + b\)
\(y=-\frac{6}{5}x + 2\)

Answer:

\(y =-\frac{6}{5}x + 2\)