Linear Functions• I can determine if a graph, table or

equation is a linear function.• I can find the equation of a linear

function.• I can interpret the values in a linear

function.

Linear Functions

Modeling with linear functions.

• Example: Suppose the operating costs of the cafeteria are $3000 for one day. If everyone’s lunch is $2.65, how many lunches have to be purchased for the cafeteria to break even? • f(x) = -3,000 + 2.65x • 0 = -3,000 + 2.65x• 3,000 = 2.65x• x = 1,133 lunches to break even

Your Turn• Take a couple minutes to come up with your

own scenario that models a linear function. • Use y=mx+b as your model. And describe your

model• Once written down, exchange with a neighbor• Have your neighbor:• State whether the rate of change is constant.• State whether the slope-intercept (b) value makes

sense.

Let t be the number of years since 1970. Suppose the population was 23,000 people in 1982 and 21,000 in 1986. Assuming the population has been declining at a constant rate since 1970.

a. Find the formula for population as a function of t.

b. When will the population be zero people?

To determine if a function is linear…• View it graphically• Look at it algebraically (equation)• Numerically as a table and check for constant rate of

change.