Question
Keylie is a freelance web designer. She charges her clients a $35 consulting fee plus $45 per hour worked.
The function that represents this situation is f(x) = 45x + 35
. Which graph accurately represents how much money Keylie will make if she has to work for 4, 6, 8, 10, and 12 hours for a client?
(1 point)
Responses
The function that represents this situation is f(x) = 45x + 35
. Which graph accurately represents how much money Keylie will make if she has to work for 4, 6, 8, 10, and 12 hours for a client?
(1 point)
Responses
Answers
Answered by
GPT-4o mini
To determine how much money Keylie will make for different hours worked, we can calculate the total fee for each specified number of hours (x) based on the function provided:
\[ f(x) = 45x + 35 \]
Now we will calculate f(x) for x = 4, 6, 8, 10, and 12:
1. For **4 hours**:
\[
f(4) = 45(4) + 35 = 180 + 35 = 215
\]
2. For **6 hours**:
\[
f(6) = 45(6) + 35 = 270 + 35 = 305
\]
3. For **8 hours**:
\[
f(8) = 45(8) + 35 = 360 + 35 = 395
\]
4. For **10 hours**:
\[
f(10) = 45(10) + 35 = 450 + 35 = 485
\]
5. For **12 hours**:
\[
f(12) = 45(12) + 35 = 540 + 35 = 575
\]
Summarizing these results:
- At **4 hours**: $215
- At **6 hours**: $305
- At **8 hours**: $395
- At **10 hours**: $485
- At **12 hours**: $575
### Creating the Graph
Now, plot these points on a graph where the x-axis represents the number of hours worked (4, 6, 8, 10, 12) and the y-axis represents the amount of money made:
- Point (4, 215)
- Point (6, 305)
- Point (8, 395)
- Point (10, 485)
- Point (12, 575)
You should see a linear graph increasing as the number of hours worked increases, consistent with the linear function provided.
If you have options for graphs, the correct one will show these points and clearly represent a straight line going upwards through these coordinates.
\[ f(x) = 45x + 35 \]
Now we will calculate f(x) for x = 4, 6, 8, 10, and 12:
1. For **4 hours**:
\[
f(4) = 45(4) + 35 = 180 + 35 = 215
\]
2. For **6 hours**:
\[
f(6) = 45(6) + 35 = 270 + 35 = 305
\]
3. For **8 hours**:
\[
f(8) = 45(8) + 35 = 360 + 35 = 395
\]
4. For **10 hours**:
\[
f(10) = 45(10) + 35 = 450 + 35 = 485
\]
5. For **12 hours**:
\[
f(12) = 45(12) + 35 = 540 + 35 = 575
\]
Summarizing these results:
- At **4 hours**: $215
- At **6 hours**: $305
- At **8 hours**: $395
- At **10 hours**: $485
- At **12 hours**: $575
### Creating the Graph
Now, plot these points on a graph where the x-axis represents the number of hours worked (4, 6, 8, 10, 12) and the y-axis represents the amount of money made:
- Point (4, 215)
- Point (6, 305)
- Point (8, 395)
- Point (10, 485)
- Point (12, 575)
You should see a linear graph increasing as the number of hours worked increases, consistent with the linear function provided.
If you have options for graphs, the correct one will show these points and clearly represent a straight line going upwards through these coordinates.
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