Question

directions: analyze the graphs, and solve the linear equation questions. show all steps when solving. use figure 1 for questions 1 and 2. 1. write a system of equations represented by these two lines.

Explanation:

Step1: Find line 1's slope

Choose two points on the steeper line, e.g., $(0, 0)$ and $(5, 20)$.
Slope $m_1 = \frac{20-0}{5-0} = 4$.
Y-intercept $b_1=0$, so equation: $y=4x$.

Step2: Find line 2's slope

Choose two points on the gentler line, e.g., $(0, 10)$ and $(10, 30)$.
Slope $m_2 = \frac{30-10}{10-0} = 2$.
Y-intercept $b_2=10$, so equation: $y=2x+10$.

Answer:

The system of equations is:

$$\begin{cases} y = 4x \\ y = 2x + 10 \end{cases}$$