# Slopes Don’t Have to be Positive

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Graph a Linear Relationship.

Noah put $40 on his fare card. Every time he rides public transportation,$2.50 is subtracted from the amount available on his card.

(1). How much money, in dollars, is available on his card after he takes 0 rides?

(2). How much money, in dollars, is available on his card after he takes 1 ride?

(3). How much money, in dollars, is available on his card after he takes 2 rides?

(4). How much money, in dollars, is available on his card after he takes rides?

(5). Graph the relationship between amount of money on the card and number of rides.

(1). How many rides can Noah take before the card runs out of money?

(1). Where do you see this number of rides on your graph?

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Interprete the Graph of a Linear Relationship.

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.

(1). Describe what happened with the amount on Han’s fare card in July.

(2). Write an equation that represents the amount on the card in July,  and days., after  days.

(3). What value makes sense for the slope of the line that represents the amounts on Han’s fare card in July?

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Draw Graphs of Linear Relations.

• Interact with the applet below by moving points A and B to two points on the axes that belong to the given relation.​ You will see a comment if the points are correct.
• Click on to do more.
• Continue as much as you can.

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(1). 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?

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Suppose that during its flight, the elevation e (in feet) of a certain airplane and its time t , in minutes since takeoff, are related by a linear equation. Consider the graph of this equation, with time represented on the horizontal axis and elevation on the vertical axis. For this situation, decide if the slope is positive, zero, or negative.

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Elena’s aunt pays her \$1 for each call she makes to let people know about her aunt’s new business. The table shows how much money Diego receives for washing windows for his neighbors.