Question

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

Explanation:

Step1: Identify slope-intercept form

The standard form for a line is $y = mx + b$, where $m$ is slope, $b$ is y-intercept.

Step2: Find first line's parameters

For the rising line: y-intercept $b=3$. Slope $m=\frac{3-0}{0-(-3)}=1$.
Equation: $y = 1x + 3$ or $y = x + 3$

Step3: Find second line's parameters

For the falling line: y-intercept $b=3$. Slope $m=\frac{3-0}{0-2}=-1.5=-\frac{3}{2}$.
Equation: $y = -\frac{3}{2}x + 3$

Answer:

The system of equations is:

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