Linear Equations in Gift Card Balance
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Questions and Answers

Which linear equation correctly models the situation involving Rachel's gift card and the pounds of apples she buys?

  • y - 3.61 = -1.49(x - 3)
  • y - 15.53 = -1.49(x - 11)
  • y - 3 = -1.49(x - 15.53)
  • y - 3.61 = -1.49(x - 11) (correct)
  • What does the y-intercept represent in this context?

  • The cost of a single pound of apples
  • The amount left on the gift card after buying 3 pounds of apples
  • The maximum number of pounds of apples Rachel can buy
  • The total amount Rachel initially had on her gift card (correct)
  • What does the x-intercept indicate in terms of Rachel's purchasing capabilities?

  • The remaining balance on her gift card after purchasing apples
  • The number of pounds of apples she can buy before the gift card balance reaches $0 (correct)
  • The amount of money spent on apples
  • The total number of apples she purchased
  • What does the slope of the linear function represent in this scenario?

    <p>The rate at which the balance decreases for each additional pound of apples purchased</p> Signup and view all the answers

    If Rachel buys 0 pounds of apples, how much money remains on her gift card?

    <p>$15.53</p> Signup and view all the answers

    Study Notes

    Linear Equation for Gift Card Balance

    • The 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 purchased (x) and the remaining balance on the gift card (y).

    Y-Intercept Meaning

    • The y-intercept is the original value of the gift card to the Arbor Day Orchard.
    • This means the initial value of the gift card is the y-value when x equals 0.

    X-Intercept Meaning

    • The x-intercept is the maximum number of pounds of apples Rachel can purchase.
    • This means the x-value when y equals 0 represents the maximum number of pounds she can purchase before running out of money on the gift card.

    Slope Meaning

    • The slope represents the rate at which the amount of money remaining on the gift card decreases by $1.49 for each pound of apples Rachel buys.
    • This negative slope indicate that the balance on the gift card is decreasing as more apples are bought.

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    Description

    Explore the relationship between the pounds of apples purchased and the remaining gift card balance through linear equations. Understand the significance of the y-intercept, x-intercept, and slope in this real-world application.

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