Use the image to answer the question.

Question

A coordinate plane's x-axis ranges from 0 to 30 by 10-unit increments and its y-axis ranges from 0 to 600 by 200-unit increments. A diagonal line is plotted.

The graph models the descent of a hot air balloon in feet per minute. What does the y-intercept tell you in this situation?

(1 point)
Responses

The balloon takes 0 minutes to descend 600 feet.
The balloon takes 0 minutes to descend 600 feet.

The balloon rises 600 feet.
The balloon rises 600 feet.

The balloon starts its descent at 600 feet.
The balloon starts its descent at 600 feet.

It will take the balloon 600 minutes to descend.

Answer 1

The y-intercept of the graph represents the initial value of the variable being measured when the independent variable is zero. In this case, the y-intercept corresponds to the height of the hot air balloon when the time (x-axis) is 0 minutes.

Therefore, the correct interpretation of the y-intercept in this situation is:

The balloon starts its descent at 600 feet.

Answer 2

A rental truck company charges $25 to rent a truck, then $1.25 for every mile it is driven. The situation can be expressed as C=1.25m+25
, where C
is the total cost to rent the truck and m is the miles driven. If you plot points on the linear function, which of the following would appear?(1 point)
Responses

(4,30)
and (8,35)
left parenthesis 4 comma 30 right parenthesis and left parenthesis 8 comma 35 right parenthesis

(2,2.5)
and (4,5)
left parenthesis 2 comma 2.5 right parenthesis and left parenthesis 4 comma 5 right parenthesis

(2,22.5)
and (4,20)
left parenthesis 2,22.5 right parenthesis and left parenthesis 4 comma 20 right parenthesis

(30,4)
and (35,8)

Answer 3

To determine which points are on the line represented by the equation \( C = 1.25m + 25 \), we can plug in the values of \( m \) from each of the proposed points and see if the corresponding value of \( C \) matches.

1. For the point \( (4, 30) \): \[ C = 1.25(4) + 25 = 5 + 25 = 30 \quad \text{(This point is on the line)} \]

2. For the point \( (8, 35) \): \[ C = 1.25(8) + 25 = 10 + 25 = 35 \quad \text{(This point is on the line)} \]

3. For the point \( (2, 2.5) \): \[ C = 1.25(2) + 25 = 2.5 + 25 = 27.5 \quad \text{(Not on the line)} \]

4. For the point \( (4, 5) \): \[ C = 1.25(4) + 25 = 5 + 25 = 30 \quad \text{(Already checked)} \]

5. For the point \( (2, 22.5) \): \[ C = 1.25(2) + 25 = 2.5 + 25 = 27.5 \quad \text{(Not on the line)} \]

6. For the point \( (4, 20) \): \[ C = 1.25(4) + 25 = 5 + 25 = 30 \quad \text{(Not on the line)} \]

7. For the point \( (30, 4) \): \[ C = 1.25(30) + 25 = 37.5 + 25 = 62.5 \quad \text{(Not on the line)} \]

8. For the point \( (35, 8) \): \[ C = 1.25(35) + 25 = 43.75 + 25 = 68.75 \quad \text{(Not on the line)} \]

The only points that satisfy the equation are \( (4, 30) \) and \( (8, 35) \).

Thus, the correct answer is:

(4, 30) and (8, 35).