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Questions and Answers
Which linear equation correctly models the situation where x is the number of pounds of apples bought and y is the amount left on the gift card?
Which linear equation correctly models the situation where x is the number of pounds of apples bought and y is the amount left on the gift card?
- y - 15.53 = -1.49(x - 11)
- y - 3 = -1.49(x - 3.61)
- y - 3.61 = -1.49(x - 3)
- y - 3.61 = -1.49(x - 11) (correct)
What does the y-intercept represent in the context of the gift card?
What does the y-intercept represent in the context of the gift card?
- The amount left after buying the minimum number of pounds.
- The amount Rachel spent buying apples.
- The maximum number of pounds of apples Rachel can buy.
- The original value of the gift card. (correct)
What is the meaning of the x-intercept in this situation?
What is the meaning of the x-intercept in this situation?
- The total weight of apples Rachel can buy.
- The maximum weight of apples Rachel can purchase with her gift card.
- The amount spent if all funds were used to buy apples.
- The ending value of the gift card when no apples remain. (correct)
What does the slope of the equation represent?
What does the slope of the equation represent?
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If Rachel bought 5 pounds of apples, how much would be left on her gift card using the derived model?
If Rachel bought 5 pounds of apples, how much would be left on her gift card using the derived model?
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Study Notes
Linear Equation for Apple Purchases
- The correct linear equation that models the situation is y-3.61 = -1.49(x-11)
- This equation represents the relationship between the number of pounds of apples Rachel buys (x) and the amount left on her gift card (y).
Y-Intercept Meaning
- The y-intercept represents the original value of the gift card to the Arbor Day Orchard.
- In this case, the y-intercept is the amount of money on the gift card when Rachel has bought zero pounds of apples.
X-Intercept Meaning
- The x-intercept represents the maximum number of pounds of apples Rachel can purchase.
- At the x-intercept, the amount remaining on the gift card is zero, meaning Rachel has spent all of the gift card's value.
Slope Meaning
- The slope of the line (-1.49) represents the changing value of the gift card.
- For each pound of apples Rachel buys, the amount remaining on the gift card decreases by $1.49.
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