Keylie is a freelance web designer. She charges her clients a $20 consulting fee plus $45 per hour worked. If they need images, Keylie charges an additional $15 fee for image research. 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 and has to find images?(1 point)

Question

Responses

Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from 0 to 15 in increments of 5. The y-axis ranges from 0 to 600 in increments of 100.
Image with alt text: Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from 0 to 15 in increments of 5. The y-axis ranges from 0 to 600 in increments of 100.

Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from 0 to 600 in increments of 100. The y-axis ranges from 0 to 12 in increments of 2.
Image with alt text: Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from 0 to 600 in increments of 100. The y-axis ranges from 0 to 12 in increments of 2.

Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from 0 to 15 in increments of 5. The y-axis ranges from 0 to 100 in increments of 20.
Image with alt text: Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from 0 to 15 in increments of 5. The y-axis ranges from 0 to 100 in increments of 20.

Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from 0 to 15 in increments of 5. The y-axis ranges from 0 to 600 in increments of 100.
Image with alt text: Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from 0 to 15 in increments of 5. The y-axis ranges from 0 to 600 in increments of 100.
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Answer 1

To determine how much money Keylie will make based on her pricing structure, we need to calculate her total charge for various hours worked along with the image research fee.

Keylie's total charge can be calculated using the following formula:

\[ \text{Total Charge} = \text{Consultation Fee} + (\text{Hourly Rate} \times \text{Hours Worked}) + \text{Image Research Fee} \]

Given:

• Consultation Fee = $20
• Hourly Rate = $45
• Image Research Fee = $15
• Hours Worked = 4, 6, 8, 10, and 12

Now we can calculate her total charge for each of the hour increments:

1. For 4 hours: \[ \text{Total} = 20 + (45 \times 4) + 15 = 20 + 180 + 15 = 215 \]

2. For 6 hours: \[ \text{Total} = 20 + (45 \times 6) + 15 = 20 + 270 + 15 = 305 \]

3. For 8 hours: \[ \text{Total} = 20 + (45 \times 8) + 15 = 20 + 360 + 15 = 395 \]

4. For 10 hours: \[ \text{Total} = 20 + (45 \times 10) + 15 = 20 + 450 + 15 = 485 \]

5. For 12 hours: \[ \text{Total} = 20 + (45 \times 12) + 15 = 20 + 540 + 15 = 575 \]

Now we have the following points representing how much money she will make based on hours worked:

• (4, 215)
• (6, 305)
• (8, 395)
• (10, 485)
• (12, 575)

Next, we need to determine which graph accurately represents these points and their corresponding range values.

Checking the Y-values: 215, 305, 395, 485, 575 all easily fit within the range of 0 to 600 on the y-axis in increments of 100.

Looking at the x-values (4, 6, 8, 10, 12), we need a graph with x ranging from 0 to at least 15 in increments of 5.

From this analysis, the graph that best matches the calculated values (with appropriate ranges on both axes) is:

Response: The first option with the x-axis ranging from 0 to 15 in increments of 5 and the y-axis ranging from 0 to 600 in increments of 100.

This option will accurately represent Keylie's earnings based on the input values.

Answer 2

ABC or d

Answer 3

Based on the calculations and analysis provided, the correct option that accurately represents how much money Keylie will make based on her working hours is:

Option A: The graph with the x-axis ranging from 0 to 15 in increments of 5 and the y-axis ranging from 0 to 600 in increments of 100.

If you have specific labels or letters (A, B, C, D) for the graph options, please indicate them, and I can confirm explicitly which one it matches. But based on the graphs described earlier, the first option fits best.

Answer 4

Use the image to answer the question.

A line graph which shows X-axis ranging from 0 to 15 in increments of 5 and y-axis ranging from 0 to 30 in increments of 10.

Colin charges a flat fee for babysitting plus an hourly fee. His total cost is represented on the graph. How can you represent this situation algebraically?

(1 point)
y=
x+
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Answer 5

To represent Colin's babysitting charges algebraically, we first need to analyze the components of the total cost.

Assuming the line graph shows the relationship between hours worked (x) and total cost (y):

1. Flat Fee: This is the fixed amount Colin charges regardless of hours worked. It would be the y-intercept of the line on the graph, which is the value of \(y\) when \(x = 0\).

2. Hourly Fee: This is the amount charged per hour, which is represented by the slope of the line. You can calculate the slope by finding the change in \(y\) for a unit change in \(x\).

General Form of the Equation

The general form of a linear equation relating total cost (y) to hours worked (x) is:

\[ y = mx + b \]

Where:

• \(m\) is the hourly fee (slope),
• \(b\) is the flat fee (y-intercept).

Steps to Create the Equation

• Identify the flat fee (b): Look at where the line crosses the y-axis. If it intersects at 10, for example, then \(b = 10\).
• Calculate the slope (m): Choose two points on the line (for example, (0, 10) and (5, 20)). The slope \(m\) would be calculated as:

\[ m = \frac{\text{change in } y}{\text{change in } x} = \frac{20 - 10}{5 - 0} = 2 \]

If in this example, the hourly fee is $2.

Final Equation

Assuming that the flat fee is \(10\) and the hourly fee is \(2\), the equation would be:

\[ y = 2x + 10 \]

Substitute in the Proper Structure

Now, if you need to fill in your response structured as \(y = x + \) (which seems to suggest you're looking for a specific form), you would adjust appropriately based on your slope.

If:

• The hourly fee \(m = 2\)
• The flat fee \(b = 10\)

Then in the format provided in your question, it would be:

\[ y = 2x + 10 \]

Please replace \(2\) and \(10\) with the actual values as applicable in the context of the graph if it shows different specifics for the flat fee and the hourly rate you observe in the line graph.

Answer 6

Use the image to answer the question.

A coordinate plane's x-axis ranges from negative 30 to 40 and is labeled 'Miles driven.' The y-axis ranges from 0 to 25 and is labeled 'Gallons of gas.' Both axes are divided into increments of 5. A diagonal line is plotted.

Steve made this graph to show how much gas was left in the gas tank of his truck as he drove. Did he use the appropriate scale for his axes? Enter 1 for yes or 2 for no.

(1 point)

Answer 7

To determine whether Steve used an appropriate scale for his axes, you want to consider the context of the graph:

1. X-axis (Miles driven): The range from -30 to 40 miles is unusual for a typical driving scenario, especially if negative values represent miles driven backward or distances that generally don't apply to most driving contexts. However, if negative values are just a representation and the focus is on distances driven, it may not necessarily be inappropriate. Still, acknowledging negative distances in this context might be confusing for the viewer.

2. Y-axis (Gallons of gas): Having a range from 0 to 25 gallons is reasonable, as trucks can have varying tank sizes. However, it depends on the type of truck and how far the gallons of gas adequately represent the distance driven.

To decide if the scale is appropriate:

• If the negative range on the x-axis makes sense in the context of the graph or the story being told, it might be fine.
• If the scale does not realistically match what one would expect for miles driven relative to gas consumption, it may not be appropriate.

Given the unique nature of including negative mileage and possible confusion regarding the y-axis gallons compared to those distances:

Answer: Enter 2 for no, as the graph likely does not portray an appropriate or conventional scale for the context of driving and gas consumption.

Answer 8

The city’s water company charges a fee of $20 a month in addition to a $0.25 per every gallon used. Using the function c=0.25x+20
, where c is the total cost per month for water services and x is gallons used, which of the following points on the graph accurately represents a monthly usage of 1,200 gallons?(1 point)
Responses

(1,200,300)
left parenthesis 1,200 comma 300 right parenthesis

(1,200,−180)
left parenthesis 1,200 comma negative 180 right parenthesis

(320,1,200)
left parenthesis 320 comma 1,200 right parenthesis

(1,200,320)

Answer 9

To determine which point accurately represents a monthly usage of 1,200 gallons in the cost function \( c = 0.25x + 20 \), we need to substitute \( x = 1,200 \) into the function and calculate the total cost \( c \).

Calculating the total cost:

\[ c = 0.25(1200) + 20 \]

Now, calculate \(0.25 \times 1200\):

\[ 0.25 \times 1200 = 300 \]

Now, add the flat fee of $20:

\[ c = 300 + 20 = 320 \]

The total cost for 1,200 gallons of water usage is $320.

Evaluating the Response Options:

Now we will compare the calculated values to each of the given points:

1. (1,200, 300): This represents 1,200 gallons and a cost of $300 (Incorrect).
2. (1,200, -180): This represents 1,200 gallons and a cost of $-180 (Incorrect).
3. (320, 1,200): This represents a cost of $320 and a usage of 1,200 gallons (Incorrect, incorrectly formatted).
4. (1,200, 320): This represents 1,200 gallons and a cost of $320 (Correct).

Conclusion:

The point that accurately represents a monthly usage of 1,200 gallons is:

(1,200, 320)

Therefore, the correct response is (1,200, 320).

Answer 10

Use the image to answer the question.

A line with an arrow at the top is plotted in quadrant 1 of a coordinate plane. The x-axis is labeled Hours, and the y-axis is labeled Amount in Dollars.

The graph illustrates how much Amanda makes watching her little cousins. Using the graph, predict how much Amanda will make if she watches them for seven hours.

(1 point)
Responses

$105
$105

$70
$70

$110
$110

$75
$75
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Answer 11

To predict how much Amanda will make if she watches her cousins for seven hours using the graph, you need to locate the point on the x-axis that corresponds to 7 hours and then trace it up to the line plotted on the graph to find the corresponding y-value. The y-value will indicate the amount in dollars that Amanda makes for those 7 hours of work.

Since I do not have access to the specific graph, I can guide you on how to answer the question based on the steps:

1. Locate 7 hours on the x-axis.
2. Move up vertically to where this point intersects the line.
3. Read the corresponding value on the y-axis to find out how much Amanda makes.

Since I cannot see the graph, I cannot give you the exact answer. However, based on your responses ($105, $70, $110, $75), you should follow the steps above with the graph to determine which of those amounts corresponds to the y-value at 7 hours.

Check where the line intersects with the y-axis at 7 hours and pick the corresponding dollar amount from the given options. Let me know what you find, and I can help confirm if it's correct!