At an amusement park, a booth was selling soft drinks. By two pm, 37 soft drinks were sold, and by four pm, 69 were sold. Assuming that the booth was selling at a linear rate during this period, determine the slope of the line representing this information.
Let’s make a sketch of the line that would represent this information. We’ll have our 𝑥-axis that represents the time and our 𝑦-axis that represents the drinks sold. At two pm, 37 drinks had sold. And at four pm, 69 drinks had sold. We’re just doing a rough sketch of this graph. So I’m just going to leave this as 37 and 69 for these two points instead of completely labelling the 𝑦-axis. This sketch let’s us see that the longer the time goes, the more the drinks sell. But to find the slope of this line, we need to see the changes in 𝑦 over the changes in 𝑥.
For us, that would be the changes in the drinks sold over the change in time. The changes in 𝑦 can be found by subtracting 69 from 37. Doing that gives us the distance, the amount between 69 and 37. And then we can subtract four from two which gives us the time that has passed between two and four. 69 minus 37 equals 32. four minus two equals two. 32 drinks sold in two hours. But we can reduce the fraction 32 over two. Both the numerator and the denominator here are divisible by two. 32 divided by two equals 16. And two divided by two equals one. 16 over one equals 16. The slope, which represents the changes in 𝑦 over the changes in 𝑥, in this case would be equal to 16.