PLEASE HELP ME WITH MY HOMEWORK MODELING LINEAR INEQUALITIES
Algebra

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Hello! Hope you are having a good day.
Some of the answers are written in, but I will explain each part.
Part a asks you to write a function, C(g) which takes as input the amount of gas required and outputs the total cost of the trip. From the problem statement, he pays the $40 for food and entertainment, and the price of gas increases by the gallon. So the price will be $40 plus (the number of gallons * price per gallon). So, C(g) = 40 + 3.25*g = 3.25*g + 40.
For part b, the independent variable is the input, g, the amount of gas, and the dependent variable is the output, C, the total cost of the trip.
For part c, we notice that C(g) takes the form of a linear function of the form C(g) = m*g+b. For a function of this form, the slope or rate of change is m = 3.25, and the yintercept is b = 40. The yintercept represents the minimum cost, or the cost where 0 gallons of gas are required. The rate of change represents how quickly the price increases as the amount of gas required increases.
For part d, the graph looks correct. One way to graph the function would be to mark the yintercept (0,40) and mark one other point on the graph. 20 is the next marked value on the xaxis, so plug in g=20 to your function to get C(20) = 3.25*20+40=105. Then mark the point (20,105), and draw the line connecting the two marked points.
Please let me know if you need any clarification. I'm always happy to answer your questions.Secure Information
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