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 𝑥 is
graphed on the 𝑥𝑦-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 𝑥, we can say that 𝑦 is equal to 1200 plus 130𝑥. This is a linear equation of the
form 𝑦 equals 𝑚𝑥 plus 𝑏, where 𝑚 is the slope or gradient and 𝑏 is the
𝑦-intercept. In our case, the value for 𝑏 is
1200. And our value for 𝑚 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
𝑥𝑦-plane, the 𝑥-axis represents the number of days and the 𝑦-axis represents the
total budget. When 𝑥 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 𝑥 is equal to one, 𝑦 is
equal to 1330. And when 𝑥 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 130𝑥. 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 𝑥. 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.
