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.

(1 point)
y=
x+

Answer 1

(2,30) , (4,40)

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.

(1 point)
y=
x+

Answer 2

Use the table to answer the question.

x f(x)
−1
0
1
2
Finish creating the input-output table for the function f(x)=−(x+1)2+4 . Which of the given x values produces the largest output for the function?

(1 point)
Responses

x=1
x equals 1

x=0
x equals 0

x=−1
x equals negative 1

x=2

Answer 3

To complete the equation \( y = mx + b \) for Luis's paddleboat rental situation, we need to identify two key pieces of information from the graph:

1. The hourly fee (m), which represents the slope of the line, and
2. The deposit (b), which is the y-intercept, or the initial amount he pays even before he starts using the paddleboat.

Since I cannot see the graph, please provide the hourly fee and the total deposit amount, and I can help you fill in the equation with those values. For example, if the hourly fee is $5 and the deposit is $10, the equation would be:

\[ y = 5x + 10 \]

Where \( y \) is the total cost, \( x \) is the number of hours the paddleboat is rented, 5 is the hourly fee, and 10 is the deposit. Let me know the values, and I'll assist you further!

Answer 4

To derive the equation from the points (2, 30) and (4, 40), we can first determine the slope (m) and then find the y-intercept (b).

1. **Calculate the slope (m):**

Using the formula for slope:

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

Using the points (2, 30) and (4, 40):

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

So, the hourly fee is $5.

2. **Find the y-intercept (b):**

We can use one of the points to find b. We'll use the point (2, 30):

Using the equation of a line \( y = mx + b \):

\[
30 = 5(2) + b
\]
\[
30 = 10 + b
\]
\[
b = 30 - 10 = 20
\]

So, the deposit is $20.

3. **Complete the equation:**

Now we can write the equation:

\[
y = 5x + 20
\]

Thus, the completed equation for this situation is:

**y = 5x + 20**.

Answer 5

To complete the input-output table for the function \( f(x) = - (x + 1)^2 + 4 \), we will calculate the value of \( f(x) \) for each given \( x \) value: -1, 0, 1, and 2.

1. For \( x = -1 \):
\[
f(-1) = -((-1) + 1)^2 + 4 = -(0)^2 + 4 = 4
\]

2. For \( x = 0 \):
\[
f(0) = -((0) + 1)^2 + 4 = -1^2 + 4 = -1 + 4 = 3
\]

3. For \( x = 1 \):
\[
f(1) = -((1) + 1)^2 + 4 = -2^2 + 4 = -4 + 4 = 0
\]

4. For \( x = 2 \):
\[
f(2) = -((2) + 1)^2 + 4 = -3^2 + 4 = -9 + 4 = -5
\]

Now, we can summarize the output values:

| x | f(x) |
|-----|------|
| -1 | 4 |
| 0 | 3 |
| 1 | 0 |
| 2 | -5 |

### Largest Output:
The largest output value from this function occurs when \( x = -1 \), yielding \( f(-1) = 4 \).

Therefore, the response is:

**x = -1**