Linear Functions
Student Summary
Suppose a car is traveling at 30 miles per hour. The relationship between the time in hours and the distance in miles is a proportional relationship.
We can represent this relationship with an equation of the form d=30t, where distance is a function of time (since each input of time has exactly one output of distance).
Or we could write the equation t=301d instead, where time is a function of distance (since each input of distance has exactly one output of time).
More generally, if we represent a linear function with an equation like y=mx+b, then b is the initial value (which is 0 for proportional relationships), and m is the rate of change of the function.
If m is positive, the function is increasing.
If m is negative, the function is decreasing.
If we represent a linear function in a different way, say with a graph, we can use what we know about graphs of lines to find the m and b values and, if needed, write an equation.
Visual / Anchor Chart
