Introduction: Equation of a line
Opening problem
Suppose a theme park charges a $10 entrance fee, and $6 for each ride.
We can construct a table of values to show how the total cost ($y) is related to the number of rides x:
In the next applet, plot the points (x,y) and observe the shape they make.
To plot them, write them as a pair (x,y) in the + entry bar and hit Enter.
| Number of rides (x) | 0 | 1 | 2 | 3 | 4 |
| Total cost ($y) | 10 | 16 | 22 | 28 | 34 |
| | +6 | +6 | +6 | +6 | |
Plot the points
When we plot these points (x,y) on a Cartesian plane, we see that they lie on a straight line. We say that the relationship between the variables is linear.
Choose the right expression
What is the equation of the line that represents the total cost $y in terms of the number of rides x?