Video: US-SAT04S4-Q17-712176404837

Kevin is planning his summer vacation. He is interested in visiting one of the following cities: Singapore, Istanbul, or Bali. He gathered information from the Internet to help him decide the budget needed for his vacation. The given table shows the flight ticket prices for each of the three cities as well as the daily expenses needed for food and accommodation. Kevin can estimate the budget, 𝑦, in dollars. The relationship between the budget for traveling to Istanbul in dollars 𝑦 and the number of days of the vacation π‘₯ is graphed on the π‘₯𝑦-plane. What does the slope of the line represent?

03:24

Video Transcript

Kevin is planning his summer vacation. He is interested in visiting one of the following cities. Singapore, Istanbul or Bali. He gathered information from the Internet to help him decide the budget needed for his vacation. The given table shows the flight ticket prices for each of the three cities as well as the daily expenses needed for food and accommodation. Kevin can estimate the budget, 𝑦, in dollars. The relationship between the budget for traveling to Istanbul in dollars 𝑦 and the number of days of the vacation π‘₯ is graphed on the π‘₯𝑦-plane. What does the slope of the line represent?

Let’s consider the information in the table about Istanbul. The flight ticket price to Istanbul is 1200 dollars. The daily expenses are 30 pound for food and 100 pound for accommodation. This is a total of 130 pound. As the total budget is 𝑦 and the number of days is π‘₯, we can say that 𝑦 is equal to 1200 plus 130π‘₯. This is a linear equation of the form 𝑦 equals π‘šπ‘₯ plus 𝑏, where π‘š is the slope or gradient and 𝑏 is the 𝑦-intercept. In our case, the value for 𝑏 is 1200. And our value for π‘š is 130.

We were asked what the slope of the line represents. In this case, the 130 dollars represent the total daily expenses. It is the daily food and accommodation cost. We can also show this by sketching the graph. When drawing the graph in the π‘₯𝑦-plane, the π‘₯-axis represents the number of days and the 𝑦-axis represents the total budget. When π‘₯ is equal to zero, 𝑦 is equal to 1200, as 130 multiplied by zero equals zero. This confirms that the 𝑦-intercept is at 1200. When π‘₯ is equal to one, 𝑦 is equal to 1330. And when π‘₯ is equal to two, 𝑦 is equal to 1460. The total budget increases by 130 dollars per day.

Drawing a straight line through these three points gives us the linear equation 𝑦 is equal to 1200 plus 130π‘₯. This is the relationship between the number of days and the total budget for the vacation. The slope is equal to the change in 𝑦 divided by the change in π‘₯. This is equal to 130 over one, which is 130 dollars. This, once again, corresponds to the daily food and accommodation cost, as 30 plus 100 is 130.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.