Question

Luis rents a paddleboat to use at West Park for the day. He has to pay a deposit and an hourly fee. Using information from the graph, enter the values that complete the equation for this situation. (2,30) (4,40) (1 point) y=() x+()

Answer 1

To find the equation that models the relationship between the number of hours Luis rents the paddleboat (x) and the total cost (y), we can use the points given: (2, 30) and (4, 40).

First, we can find the slope (m) of the line using the two points. The slope is calculated as follows:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting in our points (2, 30) and (4, 40):
- \(y_1 = 30\), \(x_1 = 2\)
- \(y_2 = 40\), \(x_2 = 4\)

Now calculate the slope:

\[
m = \frac{40 - 30}{4 - 2} = \frac{10}{2} = 5
\]

So, the hourly fee is $5, which is the slope of the line.

Next, we need to determine the y-intercept (b). We can use one of the points to find b. Let's use the point (2, 30):

The equation of a line in slope-intercept form is:

\[
y = mx + b
\]

Plugging in the slope (m = 5) and the point (2, 30):

\[
30 = 5(2) + b
\]

Now solve for b:

\[
30 = 10 + b\\
b = 30 - 10 = 20
\]

Now we have both components of the equation: the slope (5) and the y-intercept (20). The total cost equation can be written as:

\[
y = 5x + 20
\]

Thus, the completed values for the equation based on the situation are:

- \(5\) for the coefficient of \(x\),
- \(20\) for the constant term.

So the answer is:

\[
y = 5x + 20
\]