Modeling with linear equations example 2 | Linear equations and functions | 8th grade | Khan Academy | Summary and Q&A

TL;DR

Solve word problems involving graphs of lines and learn how to graph equations in the form of y = mx + b.

Key Insights

• 🤱 The total cost of a gym membership can be calculated by adding the registration fee to the product of the monthly fee and the number of months of membership.
• 👩‍🍼 The equation of a line in the form of y = mx + b can be used to represent the cost of a gym membership, where m is the slope (monthly fee) and b is the y-intercept (registration fee).
• 🏙️ The slope of a line indicates the rate of change, while the y-intercept represents the starting point.
• 🍳 The break-even point for a lemonade stand can be determined by setting the revenue (product of the price per glass and the quantity sold) equal to the cost needed to break even.

Transcript

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Questions & Answers

Q: How is the total cost of a gym membership calculated?

To calculate the total cost of a gym membership, you add the registration fee to the product of the monthly fee and the number of months you plan to stay. For example, if you stay for 2 months with a $39 monthly fee, the cost would be $200 (registration fee) + $39 x 2 (2 months) = $278.

Q: What is the slope and y-intercept of the equation that represents the cost of a gym membership?

In the equation p = 39m + 200, where p is the total cost and m is the number of months, the slope is 39 and the y-intercept (or p-intercept) is 200. The slope indicates the increase in cost for each additional month, while the y-intercept represents the cost at 0 months.

Q: How is the break-even point calculated for the lemonade stand?

To calculate the break-even point for the lemonade stand, set the equation 0.45x = 25, where x is the number of glasses of lemonade sold. Divide both sides by 0.45 to find that x = 25 ÷ 0.45 = 55.56 (rounded to 56). Therefore, they need to sell 56 glasses of lemonade to break even.

Q: How is the graph of the lemonade stand equation represented?

In the graph, the number of glasses sold (x-axis) is plotted against the amount made (y-axis). The graph is a straight line, starting from the origin, with a positive slope indicating that as the number of glasses sold increases, the amount made also increases.

Summary & Key Takeaways

• The video demonstrates how to calculate the total cost of a gym membership by creating an equation that includes registration fees and monthly fees.

• The video also illustrates how to graph a line in the form of y = mx + b using the example of a gym membership.

• Another word problem is presented, involving a lemonade stand, where the goal is to determine the number of glasses of lemonade that need to be sold to break even.