write a system of linear equations for the graph below.

Explanation:

Step1: Find slope - intercept form ($y = mx + b$) for first line

Let's assume two points on the first line: $(x_1,y_1)$ and $(x_2,y_2)$. From the graph, if we take two points on the first line, say $(0,6)$ and $(6,0)$. The slope $m_1=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 6}{6-0}=- 1$. The $y$-intercept $b_1 = 6$. So the equation of the first line is $y=-x + 6$.

Step2: Find slope - intercept form for second line

For the second line, assume two points, say $(0,2)$ and $(2,-4)$. The slope $m_2=\frac{-4 - 2}{2-0}=\frac{-6}{2}=-3$. The $y$-intercept $b_2 = 2$. So the equation of the second line is $y=-3x + 2$.

Answer:

$\begin{cases}y=-x + 6\y=-3x + 2\end{cases}$