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.

Question

(1 point)
y=
x+

Answer 1

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 2

(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 3

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 4

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 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