Final Review 1-13-12

Final Review 1-13-121. 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.

Day Original SaleWeek 1 $25 $15Week 2 $30 $25Week 3 $28 $25Week 4 $45 $39Week 5 $42 $33

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

3.1 Graphing Linear EquationsObjectives: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

Linear EquationsA linear equation is the equation of a line. It

can be written in 3 different ways.Standard-Form (Today’s focus)Slope-Intercept FormPoint-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.

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 + y2 = 25

IDENTIFYING LINEAR EQUATIONS

Example 1 BTo 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 = 32 Simplify.The equation is now in standard form, where A = 3, B = –4, and C = 32.

Identify Linear Equations

Graphing Using Interceptsx-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.

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 =4 Original equation4x – 0 = 4 Replace y with 0.

4x =4 Simplify.x =1 Divide each side by 4.

To find the y-intercept, let x = 0.4x – y = 4 Original equation

4(0) – y =4 Replace x with 0.–y =4 Simplify.

y = –4 Divide each side by –1.

Graphing Using Intercepts2x+ 5y = 10

x-intercept y-interceptLet 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)

Graphing Using Intercepts7. y = 4 + x

x-intercept y-interceptLet 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)

Graphing Using Intercepts25. x = 5y + 5

x-intercept y-interceptLet 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)

Example:Find the x- and y-intercepts of the graphed segment.A. x-intercept is 10;

y-intercept is 250B. x-intercept is 10;

y-intercept is 10C. x-intercept is 250;

y-intercept is 10D. x-intercept is 5;

y-intercept is 10

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 125B. x-intercept is 5; y-intercept is 5C. x-intercept is 125; y-intercept is 5D. x-intercept is 5; y-intercept is 10

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.

Individual PracticeDo p. 159 - 160 5, 6, 19, 21 and 12

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

X y = -1x + 2

2

y (x, y)

--4

-2

0

2

4

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.

Example: Graph using a tableY = 2x + 3

Graphing By Making A Table

x y = 2x + 3 y (x, y)

-2 Y = 2(-2) + 3

-1

0

1

2

Homework 1-13Read 3-1 Take NotesP. 159 14-28 even,

Read 3-1 Take Notes