Linear functions of slopes

Question

The linear function f(x) = 46.9x + 62.2 models the number of smartphones sold in some country, f(x), in millions, x years after 2006. Find the slope of the model. Then describe what this means in terms of the rate of change of the dependent variable per unit change in the independent variable.

Answer 1

A linear function is a function where the relationship of the dependent variable (y) to the independent variable (X) can be graphed as a line. Remember the slope intercept form of the equation of a line, y = mx + b. In this type of equation, m is the slope of the line and b is the y-intercept. In other words, m is how quickly the line rises or falls and b is the value of y when x is 0.

Your equation starts with f(x), which is another way of writing y. So think of it as saying y = 46.9x + 62.2. By doing this, you can see that it is in slope intercept form. This makes it easy to identify the slope.

Your slope is 46.9. This means that when the independent variable (x) increases by 1, the dependent variable (y) will increase by 46.9.