Question

part 1
create a graph that represents the relationship between the price (y) and hours parked (x).
dennis is attending the plant city strawberry festival. he plans to park his car in a lot from 6.00pm to 11.00pm. the lot
charges $5 for the first hour and $2 for each additional hour.

Explanation:

Step1: Determine the linear equation

The cost \(y\) has a fixed cost of \(5\) for the first hour (\(x = 1\)) and then an additional \(2\) per hour for \(x>1\). The piece - wise function is \(y=

$$\begin{cases}5, &x = 1\\5+2(x - 1),&x>1\end{cases}$$

\). Simplifying the second part: \(y=2x + 3\) for \(x>1\).

Step2: Find key points

For \(x = 1\), \(y = 5\). For \(x = 2\), \(y=2\times2 + 3=7\). For \(x = 3\), \(y=2\times3+3 = 9\). For \(x = 4\), \(y=2\times4 + 3=11\). For \(x = 5\), \(y=2\times5+3 = 13\).

Step3: Plot the graph

On the \(x\) - axis (hours parked) and \(y\) - axis (price), plot the point \((1,5)\). Then, for \(x>1\), since \(y = 2x+3\) (a linear function with slope \(m = 2\) and \(y\) - intercept \(b = 3\)), draw a line starting from the point \((1,5)\) (with an open - circle at \(x = 1\) for the part \(y=2x + 3\)) and passing through \((2,7)\), \((3,9)\), etc.

Answer:

The graph has a point at \((1,5)\) and a line \(y = 2x+3\) for \(x>1\) (with an open - circle at \(x = 1\) for the linear part).