1. Final Review 1-13-12 1. The original and sale price of an item are shown below. During which week did the price change the most? 2. Which graph has a negative slope? a.b.C. D. DayOriginalSale Week 1$25$15 Week 2$30$25 Week 3$28$25 Week 4$45$39 Week 5$42$33

2. Interim Review 1-13-12 3. What is the slope of the line joining the points (6, -3) and (8,6)? 4. Simplify : 12x – 4y + 7x – 8y 5. p. 162 #68 6. p. 162 #66 7. p. 162 #67 8. p. 162 # 65

3. 3.1 Graphing Linear Equations Objectives: By the end of the period, with an 85% accuracy, students will be able to: Determine whether an equation is written in standard form Graph linear equation using the x- and y- intercepts Graph linear equations by making a table

4. Linear Equations A linear equation is the equation of a line. It can be written in 3 different ways. Standard-Form (Today’s focus) Slope-Intercept Form Point-Slope Form Linear equations in Standard Form are written in the form Ax + By = C and must satisfy 4 criteria:  A ≥ 0  A and B are not both zero  A, B and C are integers whose greatest common factor is 1.  The exponents for each variable should equal 1.

5. Determine whether the equation is a linear equation. If so, write the equation in standard form and identify A, B and C. a. 4xy + 2y = 7 b. 2x = 3y + 3 c. y = 4 – 3x d. p. 159 #1 x = y - 5 e. p. 159 #13 5x + y 2 = 25 IDENTIFYING LINEAR EQUATIONS

6. Example 1 B To write the equation with integer coefficients, multiply each term by 4. Answer: This is a linear equation. Original equation Multiply each side of the equation by 4. 3x – 4y=32Simplify. The equation is now in standard form, where A = 3, B = –4, and C = 32. Identify Linear Equations

7. Graphing Using Intercepts x-intercept - The x-coordinate where the graph crosses the x axis. To find the x-intercept, let y = 0. y-intercept - The y-coordinate where the graph crosses the y axis. To find the y-intercept, let x = 0.

8. Example Graph by Using Intercepts Graph 4x – y = 4 using the x-intercept and the y-intercept. To find the x-intercept, let y = 0. 4x – y =4Original equation 4x – 0 = 4Replace y with 0. 4x=4Simplify. x=1Divide each side by 4. To find the y-intercept, let x = 0. 4x – y = 4Original equation 4(0) – y =4Replace x with 0. –y=4Simplify. y =–4Divide each side by –1.

9. Graphing Using Intercepts 2x+ 5y = 10 x-intercept y-intercept Let y = 0 2x + 5y = 10 2x + 5(0) = 10 2x + 0 = 10 2x = 10 2 2 x = 5 x-intercept x –int. is the point (5,0) Let x = 0 2x + 5y = 10 2(0) + 5y = 10 0 + 5y = 10 5y = 10 5 5 y = 2 y-intercept y-int. is the point (0,2)

10. Graphing Using Intercepts 7. y = 4 + x x-intercept y-intercept Let y = 0 y = 4 + x 0 = 4 + x -4 -4. -4 = x x-intercept x-int. is the point (-4,0) Let x = 0 y = 4 + x y = 4 + 0 y = 4 y-intercept y-int. is the point (0, 4)

11. Graphing Using Intercepts 25. x = 5y + 5 x-intercept y-intercept Let y = 0 x = 5y + 5 x = 5(0) + 5 x = 0 + 5 x = 5 x-intercept x –int. is the point (5,0) Let x = 0 x = 5y + 5 0 = 5y + 5 -5 - 5 -5 = 5y -5 -5 -1 = y y-intercept y-int. is the point (0, -1)

12. Example: Find the x- and y- intercepts of the graphed segment. A.x-intercept is 10; y-intercept is 250 B.x-intercept is 10; y-intercept is 10 C.x-intercept is 250; y-intercept is 10 D.x-intercept is 5; y-intercept is 10

13. Example ANALYZE TABLES Jules has a gas card for a local gas station. The table shows the function relating the amount of money on the card and the number of times he has stopped to purchase gas. A. Determine the x- and y- intercepts of the graph of the function. A. x-intercept is 5; y-intercept is 125 B. x-intercept is 5; y-intercept is 5 C. x-intercept is 125; y-intercept is 5 D. x-intercept is 5; y-intercept is 10

14. Example B. Describe what the y-intercept of 125 means in the previous problem. A.It represents the time when there is no money left on the card. B.It represents the number of gas stops. C.At time 0, or before any gas stops, there was $125 on the card. D.This cannot be determined.

15. Individual Practice Do p. 159 - 160 5, 6, 19, 21 and 12

16. 9.Graph x + 2y = 4 first get y by itself x + 2y = 4 -x -x 2y = -x + 4 2 2 2 y = -1x + 2 2 Graphing By Making A Table

17. X y = -1x + 2 2 y(x, y) --4 -2 0 2 4

18. p. 159 Graph each equation. x = 3 Vertical line through the x axis at 3. Example like 9. y = 5 Horizontal line through the y axis at 5.

19. Example: Graph using a table Y = 2x + 3 Graphing By Making A Table

20. xy = 2x + 3y(x, y) -2Y = 2(-2) + 3 0 1 2

21. Homework 1-13 Read 3-1 Take Notes P. 159 14-28 even, Read 3-1 Take Notes