Question

Question 1
A)
A surf instructor has an initial fee of $12 and charges $8 per hour for lessons.

Write a linear equation that represents the total cost of surf lessons after a certain number of hours.



(1 point)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Response area
Question 2
A)
The surf instructor has an initial fee of $12 and charges $8 per hour for lessons, which is represented by the equation y=8x+12
, where x is the number of hours and y is the total cost. The instructor gives 32 hours of lessons per month to Sandra and 24 hours of lessons per month to Bela. What is the total amount the instructor makes in a month?





NOTE: Type the numerical value into the blank to receive credit. DO NOT type the $ into the blank.

(1 point)
The instructor receives $$$ per month in total from Sandra and Bela.
Question 3
A)
For the new year, the instructor is thinking of changing his rates. The equation of the possible new rates is represented in the graph. What is the y-intercept of the instructor's new rates?





NOTE: Type the x and y-coordinates into the blanks to receive credit for this question.

(2 points)
($$, $$)
Question 4
A)After a few years, the surf instructor has $3500 saved for rent. He rents an apartment that costs $275 per month. Which graph represents the equation of this scenario?(1 point)
Responses








Question 5
A)
The instructor's friend also plans to rent an apartment in the same complex. Use the graph to identify the y-intercepts, the slope, and to write an equation in slope-intercept form.



(3 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
y-intercept: Response area

Slope: Response area

Linear equation: Response area

Answer 1

**Question 1:**
A linear equation that represents the total cost \(y\) of surf lessons after a certain number of hours \(x\) is:
\[ y = 8x + 12 \]

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**Question 2:**
To find the total amount the instructor makes in a month from Sandra and Bela:
- For Sandra: 32 hours → \( y = 8(32) + 12 = 256 + 12 = 268 \)
- For Bela: 24 hours → \( y = 8(24) + 12 = 192 + 12 = 204 \)

Total amount:
\[ 268 + 204 = 472 \]

The instructor receives **472** per month in total from Sandra and Bela.

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**Question 3:**
If we are looking for the y-intercept of the instructor's new rates graph (which should be where the line crosses the y-axis), the y-coordinate (the cost when hours are 0) needs to be provided. Assuming the graph shows an intercept value (however, it is not given here), you would fill in the details accordingly. For example:
(0, $$)

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**Question 4:**
To represent the scenario where the instructor has $3500 saved for rent and pays $275 per month, we would typically need to see a graphical representation to identify the correct graph.

However, assuming the graph illustrates a decreasing line starting from the point (0,3500) and decreasing at a slope that reflects spending $275 each month, the correct graph will start at that intercept and have a negative slope.

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**Question 5:**
For the instructor's friend's rental scenario, again we’d need to analyze the graph for points.
- **y-intercept**: The y-intercept would be the initial amount saved for rent (in terms of dollars).
- **Slope**: The slope indicates how much the rent costs per month. It could be $275 if it corresponds to the same apartment rent.
- **Linear equation**: It should follow the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Let’s assume:
- y-intercept: **(0, 3500)**
- Slope: **-275**
- Linear equation: **y = -275x + 3500**

Fill in the responses based on the actual graph you are viewing.