Question

1. write the system of equations represented by this graph.

Explanation:

Step1: Recall 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.

Step2: Find equation for first line

Identify y-intercept $b=3$. Calculate slope $m=\frac{3-0}{0-(-3)}=1$.
$y = 1x + 3$ or $y = x + 3$

Step3: Find equation for second line

Identify y-intercept $b=3$. Calculate slope $m=\frac{3-0}{0-1}=-2$.
$y = -2x + 3$

Answer:

The system of equations is

$$\begin{cases} y = x + 3 \\ y = -2x + 3 \end{cases}$$