Question

example 1: a system of equations is graphed on the grid. write the system of equations that is best represented by the graph.

Explanation:

Step1: Analyze the steeper line

The steeper line passes through the origin \((0,0)\) and \((2,6)\). The slope \(m\) is calculated as \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{6 - 0}{2 - 0}=3\). Using the slope - intercept form \(y = mx + b\) (where \(b = 0\) since it passes through the origin), the equation is \(y = 3x\).

Step2: Analyze the less - steep line

The less - steep line passes through \((0,-2)\) and \((4,0)\). The slope \(m=\frac{0-(-2)}{4 - 0}=\frac{2}{4}=\frac{1}{2}\). Using the slope - intercept form \(y=mx + b\), with \(b=-2\), the equation is \(y=\frac{1}{2}x-2\).

Answer:

The system of equations is \(

$$\begin{cases}y = 3x\\y=\frac{1}{2}x-2\end{cases}$$

\)