IM 8.3.9 Lesson: Slopes Don't Have to be Positive
Which line doesn't belong?
Noah put $40 on his fare card. Every time he rides public transportation, $2.50 is subtracted from the amount available on his card.
How much money, in dollars, is available on his card after he takes 0 rides?
How much money, in dollars, is available on his card after he takes 1 ride?
How much money, in dollars, is available on his card after he takes 2 rides?
How much money, in dollars, is available on his card after he takes rides?
Graph the relationship between amount of money on the card and number of rides.
How many rides can Noah take before the card runs out of money?
Where do you see this number of rides on your graph?
Here is a graph that shows the amount on Han’s fare card for every day of last July. Plot and label 3 different points on the line.
Describe what happened with the amount on Han’s fare card in July.
Write an equation that represents the amount on the card in July, , after days.
What value makes sense for the slope of the line that represents the amounts on Han’s fare card in July?
Let’s say you have taken out a loan and are paying it back. Which of the following graphs have positive slope and which have negative slope?
Amount paid on the vertical axis and time since payments started on the horizontal axis.
Amount owed on the vertical axis and time remaining until the loan is paid off on the horizontal axis.
Amount paid on the vertical axis and time remaining until the loan is paid off on the horizontal axis.
Elena borrowed some money from her brother. She pays him back by giving him the same amount every week. The graph shows how much she owes after each week.
What is the slope of the line?
Explain how you know whether the slope is positive or negative.
What does the slope represent in this situation?
How much did Elena borrow?
How much time will it take for Elena to pay back all the money she borrowed?