Question

on your own: graph systems to solve
the graph of each function is shown.
at what point do the graphs intersect? enter your answer in the box

Explanation:

Step1: Identify equations of lines

First, find the equation for \(f(x)\): it has a y-intercept of \(4\), slope \(m=\frac{1}{1}=1\), so \(f(x)=x+4\).
For \(g(x)\): y-intercept is \(19\), slope \(m=\frac{-2}{1}=-2\), so \(g(x)=-2x+19\).

Step2: Set equations equal to each other

To find intersection, solve \(f(x)=g(x)\):
$$x+4=-2x+19$$

Step3: Solve for x

Add \(2x\) to both sides:
$$3x+4=19$$
Subtract 4 from both sides:
$$3x=15$$
Divide by 3:
$$x=5$$

Step4: Find y-value

Substitute \(x=5\) into \(f(x)\):
$$f(5)=5+4=9$$

Answer:

\((5, 9)\)