Question

write a system of linear equations for the graph below.
(there is a coordinate plane graph with two lines and a system of equations with two y=□ blanks)

Explanation:

Step1: Find equation for the first line (steeper line)

We identify two points on the steeper line: \((0, -7)\) (y-intercept) and \((2, 1)\). The slope \(m\) is calculated as \(\frac{1 - (-7)}{2 - 0} = \frac{8}{2} = 4\). Using the slope - intercept form \(y = mx + b\) (where \(b=-7\)), the equation is \(y = 4x - 7\).

Step2: Find equation for the second line (less steep line)

We identify two points on the less steep line: \((0, 2)\) (y - intercept) and \((2, 1)\). The slope \(m\) is calculated as \(\frac{1 - 2}{2 - 0}=\frac{-1}{2}=-\frac{1}{2}\). Using the slope - intercept form \(y = mx + b\) (where \(b = 2\)), the equation is \(y=-\frac{1}{2}x + 2\).

Answer:

\(

$$\begin{cases}y = 4x - 7\\y=-\frac{1}{2}x + 2\end{cases}$$

\)