Question

write a system of linear equations for the graph below.
(the graph shows two lines on a coordinate plane with x-axis from -9 to 9 and y-axis from -9 to 9. one line passes through (0,1) and (2,-5), the other passes through (0,-4) and (-8,0). there is a system of equations box with two y= equations to fill.)

Explanation:

Step1: Find the first line's equation

The steep line passes through \((0, 1)\) and \((2, -5)\). The slope \(m_1=\frac{-5 - 1}{2 - 0}=\frac{-6}{2}=-3\). Using slope - intercept form \(y = mx + b\) (where \(b\) is the y - intercept, here \(b = 1\)), the equation is \(y=-3x + 1\).

Step2: Find the second line's equation

The other line passes through \((0, - 4)\) and \((-8,0)\). The slope \(m_2=\frac{0-(-4)}{-8 - 0}=\frac{4}{-8}=-\frac{1}{2}\). Using slope - intercept form with \(b=-4\), the equation is \(y =-\frac{1}{2}x-4\).

Answer:

\(

$$\begin{cases}y=-3x + 1\\y =-\frac{1}{2}x-4\end{cases}$$

\)