Download Linear Functions Objectives: SWBAT identify linear

Linear Functions
Objectives: SWBAT identify linear functions using graphs, tables, and equations
SWBAT graph linear functions using discrete and continuous data
SWBAT write real-life problems to fit data
Linear Equation in Two Variables—an equation that can be written in the form 𝑦 = 𝑚𝑥 + 𝑏
where m and b are constants. The graph of a linear equation is a line.
Linear Function—a function whose graph is a non-vertical line
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥
Rate of Change—slope = 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦
Nonlinear Function—a function that does not have a constant rate of change. It is NOT a line
Example 1: Does the graph represent a linear or nonlinear function? Explain.
Example 2: Find the rate of change of each table to determine if it represents a linear function.
Example 3: Which of the functions below represent linear functions?
Solution of a linear equation—an ordered pair (x, y) that makes the equation true
The graph of a linear equation is the set of all points (x, y) that represents all the solutions
of the equation.
Example 4: The linear function y = 15.95x represents the cost y (in dollars) for x tickets for a
museum. Each customer can buy a maximum of four tickets.
a) Is the domain discrete or continuous? Explain.
b) Find the domain of the function.
c) Graph the function using its domain.
Example 5: A cereal bar contains 130 calories. The number c of calories consumed is a function
of the number b of bars eaten.
a) Does this situation represent a linear function? Explain.
b) Is the domain discrete or continuous? Explain.
c) Find the domain of the function.
d) Graph the function using its domain.
Example 6: Write a real-life problem to fit the data shown in each graph. Is the domain of each
function discrete or continuous? Explain.