Question

use the graphs of the linear functions on the right. write the linear system whose solution set is {(6, -2)}. express each equation in the system in slope-intercept form.

Explanation:

Step1: Recall slope-intercept form

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. Since the solution of the system is \((6,-2)\), both lines pass through the point \((x,y)=(6, - 2)\). But we need the graphs (which are not fully shown here) to determine the slopes of the two lines. Let's assume we can find two lines that pass through \((6,-2)\) from the given graphs. For example, if one line has a slope \(m_1\) and the other has a slope \(m_2\).

Step2: Determine slopes from graphs (hypothetical example)

Suppose from the graphs, one line has a slope \(m_1 = 1\) and the other has a slope \(m_2=-1\).

For the first line with \(m = 1\) and passing through \((6,-2)\):
Using the point - slope form \(y - y_1=m(x - x_1)\) (where \((x_1,y_1)=(6,-2)\))
\(y-(-2)=1\times(x - 6)\)
\(y + 2=x - 6\)
\(y=x-6 - 2\)
\(y=x - 8\)

For the second line with \(m=-1\) and passing through \((6,-2)\):
\(y-(-2)=-1\times(x - 6)\)
\(y + 2=-x + 6\)
\(y=-x+6 - 2\)
\(y=-x + 4\)

(Note: Since the actual graphs are not fully provided, this is a hypothetical example. In a real - world scenario, we would use the rise - over - run method on the given graphs to find the slopes of the two lines and then use the point \((6,-2)\) to find the y - intercepts.)

Answer:

(The answer depends on the actual slopes of the lines from the graphs. A possible system (hypothetical) is \(

$$\begin{cases}y=x - 8\\y=-x + 4\end{cases}$$

\))