The graph shows how the price of skiing lessons is discounted depending on the number of lessons purchased. Write a formula for the cost 𝑐 in terms of the number of lessons 𝑛.
The cost 𝑐 is found on the 𝑦-axis. The number of lessons 𝑛 is found on the 𝑥-axis. So notice our graph is a straight line. And the equation for a straight line is 𝑦 equals 𝑚𝑥 plus 𝑐, where 𝑚 is the gradient — the steepness — of the graph and 𝑐 is the 𝑦-intercept where the graph crosses the 𝑦-axis.
Right away, we can see that our graph crosses the 𝑦-axis at 90. So we can replace 𝑐 with 90. Now do not get this 90 confused with the cost 𝑐. 𝑐 for 90 just represents the 𝑦-intercept. Now to find the gradient 𝑚, we need to take the change in the 𝑦-values and divide by the change in the 𝑥-values.
So looking at our graph, we need to find two points that are very visible in our graph, meaning they go through an exact point on our grid, and then find the gradient between them. Here we know that our graph crosses the 𝑦-axis at zero, 90. And another place that our graph crosses is here at the point five, 46.
The small lines they represent two. That’s how we know that we were at five, 46. So from our 𝑦-values, we went from 90 to 46. That is a decrease of 44. For our 𝑥-values, we went from zero to five. That’s an increase in five. Negative forty-four fifths is not reduced. We will leave it just as it is.
However, we were asked to write a formula for the cost 𝑐 in terms of the number of lessons 𝑛. The cost 𝑐 was on our 𝑦-axis. So we can replace 𝑦 with 𝑐. And the number of lessons 𝑛 was on the 𝑥-axis. So we can replace 𝑥 with 𝑛.
Therefore, our equation will be 𝑐 equals negative forty-four fifths 𝑛 plus 90. And this should make sense because it said the graph shows how the price of skiing lessons is discounted depending on the number of lessons purchased. So notice the cost: the 𝑦-value goes down as the number of lessons increase. So the more lessons you buy, the less you have to pay per lesson.