1. Algebra 2 Chapter 2.2 Linear Relations & Functions Target Goals: 1.Identify linear relations and functions 2.Determine the intercepts of linear equations/functions 3.Graph linear equations/functions using intercepts

2. New Vocabulary Linear Relations – Relations with straight lines when graphed Linear Equation – Has no operations except addition, subtraction, & multiplication of a variable by a constant – Fractions of numbers are ok, but variable can NOT be in the denominator! – No exponents on variables other than 1 (which usually is not written)

3. Linear vs. Non-Linear Linear EquationsNon-Linear Equations

4. Function Notation vs. Equations f(x) = y f(x) replaces the dependent variable (y) y = 2x + 1  f(x) = 2x + 1

5. Characteristics of Linear Functions Graph is a straight line Only operations seen are +, -, or multiplication of variable and a constant (a number) No variables in the denominator Exponents on variables are only 1 No variables are multiplied together

6. Practice: State whether each function is a linear function. Write yes or no and explain your answer. Yes!! No – variable in the denominator No – exponent on variable is not 1

7. Connection to Order of Operations/Formulas/Real-Life! Ex 4) The linear function can be used to find the number of degrees Fahrenheit f (C) that are equivalent to a given number of degrees Celsius C. On the Celsius scale, normal body temperature is 37°C. What is it in degrees Fahrenheit?

8. INTERCEPTS y-intercept: the point where the line crosses the y-axis; (0, b) x-intercept: the point where the line crosses the x-axis; (a, 0)

9. Practice: Find the x-intercept and the y- intercept of the graph of the linear equation. Then graph the equation. Ex 5) 2x + 5y – 10 = 0 x-intercept 2x + 5y – 10 = 0 2x + 5(0) – 10 = 0 2x – 10 = 0 2x = 10 x = 5 (5, 0) y-intercept 2x + 5y – 10 = 0 2(0) + 5y – 10 = 0 5y – 10 = 0 5y = 10 y = 2 (0, 2)

10. Practice: Find the x-intercept and the y- intercept of the graph of the linear equation. Then graph the equation. Ex 6) -2x + y – 4 = 0 x-intercept -2x + y – 4 = 0 -2x + (0) – 4 = 0 -2x – 4 = 0 -2x = 4 x = -2 (-2, 0) y-intercept -2x + y – 4 = 0 -2(0) + y – 4 = 0 y – 4 = 0 y = 4 (0, 4)