3-1 Graphing Linear Equations using a table. 3-2b Graphing Linear Equations Using a TI- 84 Calculator

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2 3-1 Graphing Linear Equations using a table 3-2 Graphing Linear Equations using x and y intercepts 3-2b Graphing Linear Equations Using a TI- 84 Calculator 3-3 Slope Mid-Chapter Review 3-4 Direct Variation 3-5 Arithmetic Sequences 3-6 Proportional and Non-proportional Relationships Chapter Review

3 Constant Intercepts Linear Equation Standard Form Name: Today we will: Identify linear equations, intercepts, and zeros. Graph Linear Functions. Define it Let s look at several examples of linear equations and some that are not linear.

4 Remember Linear Rules Both variables must have the exponent of An equation cannot be linear if You Try Determine whether the following equations represents a linear function; if not, please explain why it is not linear. Graphs of Equations A graph is a picture of the relationship between two variables, in our case, the variables x and y. The graph of a linear equation is a line. The line is made up of a series of points. You can use the equation to determine these points. Graph the following equations by using at least three points on the line. y = 3x-4 y= -2x+1

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6 What s an Intercept? DEFINE IT You Try Determine the x and y intercept for the following linear functions: EX.1 3x 4y = 12 EX.2 2x + 3y = 6 Graphs of Equations A graph is a picture of the relationship between two variables, in our case, the variables x and y. The graph of a linear equation is a line. The line is made up of a series of points. The x and y intercepts are two points on the line that can be used to graph it. The x intercept is -2 and the y-intercept is 3. 7x-7y = 14

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11 Slope-Intercept Graph Equations Graph the following functions, given their equations in y=mx+b form, y= 3x-1 y=-2x+4 Graph the following functions, given a point and its slope. (1, 2), m=-1 (-2,-3), m = 2/3

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13 Direct Variation WHY? See top of pg. 180 In this lesson we will:.write and graph direct variation equations..solve Problems involving direct variation. Define it How much money can Bianca earn in 5 hours of babysitting? How many hours of babysitting will it take for Bianca to earn $295? If Bianca cannot babysit that many hours what can she do to increase her income? y=kx, where k 0 Name the constant of variation for each equation. Then find the slope of the line that passes through each pair of points. Suppose x and y vary directly, and y=9, when x=-3. Write a direct variation equation that relates x and y. y= kx Direct variation formula. Replace y with _ and x with _. Divide both sides by _. Simplify. Use the direct variation equation for find x when y = 15. Direct variation formula. Replace y with _ and x with _. Divide both sides by _. Simplify.

14 NAME: Today we will: Recognize arithmetic sequences. Relate arithmetic sequences to linear functions. A sequence is a set of numbers, called terms, in a specific order. What is the pattern of this sequence? 3, 5, 7, 9, 11,... Identify The difference between the terms is call the COMMON DIFFERENCE. It is expressed as d. This is / is not an arithmetic sequence because the difference between the terms is. 7, 5, 1, -5, ,-13,-11,-9,... This is / is not an arithmetic sequence because the difference between the terms is.

15 Explicit Formula The arithmetic sequence 1, 10, 19, 28, represents the total number of dollars Valentina has in her account after her weekly allowance is added.. a. Write an equations for the nth term of the sequence. In this sequence, the first term, a 1, is 2. Find the common difference The common difference is. Use the formula for the nth term to write an equation. b. Find the 12 th term in the sequence using the formula: a n =9n-8, so a 12 = Try it Explicit Formula: 1. Let a 1 be the first term of an arithmetic sequence with common difference, d. 2. Then the sequence is a 1, a 1 + d, a 1 +2d a 1 + (n-1) d EX.1 15, 9, 3, -3, _, _, _, _... What s the pattern? Write an explicit formula? EX.2 9.5, 11.0, 12.5, 14.0, _, _, _, _... What s the pattern? Write an explicit formula?

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17 Examples Definition Name: Today we will: Write an equation for proportional relationship. Write an equation for nonproportional relationship. Define it Proportional Relationships Characteristics Counter-Example

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19 X-Intercept Y-Intercept Zero/Root Rate of Change/Slope Name: Today we will: Review the terms for Chapter 3 Cut out the following foldables on the solid line and fold on the dotted lines. Under each Key term write/draw an example

20 Name: Today we will: Review the terms for Chapter 3 Cut out the following foldables on the solid line and fold on the dotted lines. Under each Key term write/draw an example In the middle describe how all these terms are related. Y=kx K is the constant of proportionality