Suppose a job pays $20$20 per hour. A graph of income based on hours worked is shown below. Use the graph to determine how many hours are required to earn $60$60. SolutionAgain, we can tell right away that we have a linear function. This function represents the relationship between time and money.Let’s go through our checklist of what we should look at when given graphs.What are the labels, scale, and units on the graph? What does that tell me about the situation? (View answer)What pattern do I see? Is it consistent/does it stay the same? What does that tell me about the slope? (View answer)The slope for this graph is $$ per hour.Where does the graph begin? Is it continuous? Where does it cross the y𝑦-axis (y𝑦-intercept) and what does that mean? (View answer)Therefore, the y𝑦-intercept for this graph is (( ,, )).What are my domain and range in this context? Are there any values that wouldn’t make sense? (View answer)By finding the amount of $60$60 on the vertical axis, you can follow a horizontal line through the value, until it meets the graph. Follow a vertical line straight down from there, until it meets the horizontal axis. There, the value in hours is . This means that the number of hours of work needed to earn $60 is hours.CheckQuestion 1

The graph below shows a company's profit f(x), in dollars, depending on the price of pens x, in dollars, sold by the company:Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit? (2 points)Part B: What is an approximate average rate of change of the graph from x = 3 to x = 5, and what does this rate represent? (2 points)Part C: Describe the constraints of the domain. (2 points)

The manager of a furniture factory finds that it costs $2400 to manufacture 100 chairs in one day and $4800 to produce 300 chairs in one day.(a) Express the cost C (in dollars) as a function of the number of chairs x produced, assuming that it is linear.C = 0.25d+390 Sketch the graph. (b) What is the slope of the graph?What does it represent?It represents the time (in days) to produce each additional chair.It represents the number of chairs produced.    It represents the cost (in dollars) of operating the factory daily.It represents the cost (in dollars) of producing each additional chair.(c) What is the y-intercept of the graph?What does it represent?It represents the time (in days) to produce each additional chair.It represents the number of chairs produced.    It represents the cost (in dollars) of producing each additional chair.It represents the fixed daily cost (in dollars) of operating the factory. Viewing Saved Work Revert to Last Response17.[–/6 Points]DETAILSSESSCALC2 1.2.014.MY NOTESASK YOUR TEACHERPRACTICE ANOTHERThe monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her $505 to drive 460 mi and in June it cost her $565 to drive 700 mi.(a) Express the monthly cost C as a function of the distance driven d, assuming that a linear relationship gives a suitable model.C(d) = (b) Use part (a) to predict the cost of driving 1100 miles per month.$ (c) Draw the graph of the linear function. What does the slope represent?It represents the fixed cost (amount she pays even if she does not drive).It represents the cost (in dollars) of driving.    It represents the cost (in dollars) per mile.It represents the distance (in miles) traveled.(d) What does the y-intercept represent?It represents the fixed cost (amount she pays even if she does not drive).It represents the distance (in miles) traveled.    It represents the cost (in dollars) of driving.It represents the cost (in dollars) per mile.(e) Why does a linear function give a suitable model in this situation?A linear function is suitable because the monthly cost increases as the number of miles driven decreases.A linear function is suitable because the monthly cost increases even if the miles driven is constant.    A linear function is suitable because the monthly cost is fixed despite the fact that the miles driven may vary.A linear function is suitable because the monthly cost increases as the number of miles driven

ProblemA small business has a debt of $500,000$500,000 incurred from start-up costs. It predicts that it can pay off the debt at a rate of $85,000$85,000 per year according to the following equation governing years in business (x𝑥) and debt measured in thousands of dollars (y𝑦).y=−85x+500𝑦=−85𝑥+500Graph the above equation and use your graph to predict when the debt will be fully paid. SolutionAgain it is clear from the function we wrote that this scenario represents a linear function. First, we start with creating a table of values:x𝑥y𝑦0050050011Answer 1 Question 32233033033Answer 2 Question 344160160Then we plot our points and draw the line that goes through them:Notice the scale we’ve chosen here. There’s no need to include any points above y=500𝑦=500, but it’s still wise to allow a little extra. The y𝑦-intercept of this function would be (0,(0, Answer 3 Question 3 )), which represents the amount of debt they began with.The slope, or overall pattern of a linear graph, can be found by using two points on the line. We can automatically notice that the slope will be negative, since the y𝑦-values get smaller left to right. It is always best to choose points on a graph that land close to the intervals marked, for simpler math and higher accuracy. For this reason, we’ll choose two points from our table above: (0,500)(0,500) and (3,245)(3,245). We’ll plug these in the slope formula:m=y2−y1x2−x1=245−5003−0=𝑚=𝑦2−𝑦1𝑥2−𝑥1=245−5003−0=Answer 4 Question 3 == Answer 5 Question 333Had we used our graph to find the slope, it would’ve been hard because our points are not on the intervals. The point for 33 years LOOKS like it is on 250250, but when we double check our chart, it is actually at 245245. Take a look at the scale on the y𝑦-axis. It is increasing in increments of $50$50 which makes it very difficult to determine the exact values of each point. What do you think a better scale may have been for the y𝑦-axis? [click to open]If we look at our table of values, it looks like if we used a scale of five, several of our points would now land on the intervals, making it much easier to identify the values. This would make our graph larger, but would make interpreting it much easier.While this numerical value of the slope doesn’t simplify further like we’ve previously seen, it still can give us valuable information about the pattern occurring. Remember that the slope formula represents the change in y𝑦 over the change in x𝑥, so for our problem, it represents the change in the amount of debt over the change in the number of years in business. So, we can say that for every three years in business, we can expect the debt to be reduced (go down) by 250,000250,000. (Remember, our units were in thousands of dollars.)The domain and range of this function are both Answer 6 Question 3 or x≥0𝑥≥0 and y≥0𝑦≥0. [click to open]Our output value/dependent variable is debt. Would it make sense for the amount of debt to ever go below zero? The input value/independent variable is the number of years in business. Would a company ever be in business for less than zero years? Would that make sense?Next we need to determine how many years it takes the debt to reach zero, or in other words, what x𝑥−value will make the y𝑦−value equal zero. We know it’s greater than four (since at x=4𝑥=4 the y𝑦−value is still positive), so we need an x𝑥−scale that goes well past x=4𝑥=4. Here we’ve chosen to show the x𝑥−values from 00 to 1212, though there are many other places we could have chosen to stop. We’ve also chosen a scale of 11 for the x𝑥-axis because when we count by years, we usually count by ones.To read the time that the debt is paid off, we simply read the point where the line hits y=0𝑦=0 (the x𝑥−axis). It looks as if the line hits pretty close to x=𝑥= Answer 7 Question 3. (Type a whole number.)So the debt will definitely be paid off in Answer 8 Question 3 years.CheckQuestion 3

Each time Kristine gets paid, she spends $20 and saves the rest. If the amount Kristine earns is represented by x and the amount she saves is represented by y, which graph models her savings? A graph titled Kristine's Savings has money earned on the x-axis and money saved on the y-axis. A line goes through points (5, 100) and (10, 200). A graph titled Kristine's Savings has money earned on the x-axis and money saved on the y-axis. A line goes through points (20, 1) and (40, 2). A graph titled Kristine's Savings has money earned on the x-axis and money saved on the y-axis. A line goes through points (0, 20) and (10, 30). A graph titled Kristine's Savings has money earned on the x-axis and money saved on the y-axis. A line goes through points (20, 0) and (25, 5).

Use the data shown to answer the questions that follow.Person Minutes Shopping in the Store Amount Spent on Groceries at Checkout1 46.5 140.52 55 1683 78.8 241.44 91.4 209.25 98.9 300.76 96.7 291.17 60.1 182.38 81.4 245.2 Which graph is most appropriate for these data?Group of answer choicesScatter PlotTime Series PlotBar ChartPie Chart