Think about the units for the rate of change, the x variable, and the y-intercept. How are these variables interacting? How do this affect the units?
See solution.
Practice makes perfect
In the Explore section we constructed a function that gives the value in points for a customer's card, based on the number of transactions. How can we know if the units for the function are points as we need it to be?
We can think about the structure of our function; since it is a linear equation, we can always write it in the slope-intercept form.
y = mx + b
In this equation m is the slope of the function and b is the y-intercept. In the context of this situation, the rate of change would be given in points per transaction. Then, x would be the number of transactions and b the starting amount of points. With this in mind, let's analyze the units of our function.
c c c c c c c
y&=&m&x&+&b
↓& &↓&↓& &↓&
?&=& points transaction &transaction&+&points
?&=& points transaction &transaction&+&points
?&=&points& + points & &
?&=&points& & &
y&=&points& & &
We can see that our function will have a point in units, as required.
