Two situations that can be modeled by a linear equation in the form y=mx+b are:
Monthly internet bill: The monthly cost of an internet subscription can be modeled with a linear equation, where y represents the cost and x represents the amount of data used. The equation could be y = mx + b, where m is the cost per unit of data and b is the fixed monthly cost. For example, if the cost per unit of data is $0.01 and the fixed monthly cost is $20, the equation would be y = 0.01x + 20. The variable y represents the monthly cost of the internet bill, x represents the amount of data used in the month, m represents the cost per unit of data, and b represents the fixed monthly cost.
Distance traveled by a car: The distance traveled by a car can be modeled with a linear equation, where y represents the distance and x represents the time. The equation could be y = mx + b, where m is the speed of the car and b is the initial distance traveled. For example, if the car is traveling at a speed of 60 miles per hour and has already traveled 20 miles, the equation would be y = 60x + 20. The variable y represents the distance traveled by the car, x represents the time elapsed, m represents the speed of the car, and b represents the initial distance traveled.
Here are the graphs of the two equations described above:
Monthly internet bill: Assuming the cost per unit of data is $0.01 and the fixed monthly cost is $20, the graph would look like this:
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$60 ---|------------------------
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$20 ---|-------------/------------
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0 100 200 300 400
Data used (GB)
Distance traveled by a car: Assuming the car is traveling at a speed of 60 miles per hour and has already traveled 20 miles, the graph would look like this:
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200 ---|------------------------
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100 ---|------------/------------
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20 ---|-----/------------------
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0 1 2 3 4
Time (hours)
Note that the y-axis is labeled differently in each graph to reflect the different variables being measured. Also, the zigzag line is used to indicate that the graph does not start at zero, as the values of y and x have non-zero intercepts in both cases.