Go over homework

3-5 3-5

Equations, Tables, and Equations, Tables, and GraphsGraphs

Solution

Any ordered pair that makes an equation true

(2, 6) is a solution of y = 3x because 6 = 3(2) An equation can have many solutions

(0, -8) is a solution of y = 3x – 8Because -8 = 3(0) -8 (-2, 2) is not a solution of y = 3x -8Because 2 = 3(-2) -8

Linear Equation

if all of its solutions lie on a line

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•Straight line Curvy line

Continuous line

An equation that contains two variables can be used as a rule to generate ordered pairs. When you substitute a value for x, you generate a value for y. The value substituted for x is called the input, and the value generated for y is called the output.

yy = 10= 10xx + 5 + 5

OutputOutput InputInput

In a function, the value of y (the output) is determined by the value of x (the input). All of the equations in this lesson represent functions.

Ch. 3-5 Equations, Tables, and Graphs

Example 1: Suppose you wanted to save $3 each week. Make a table and write an equation to represent your total savings after a given number of weeks. How much would you save after 15 weeks?

Number of Weeks (w)

Total Savings (t)

Equation

t = 3w

0 0 0

1 3 3(1)

2 6 3(2)

3 9 3(3)

-You need to choose a variable to represent number of weeks and total savings. Then write an equation.

The equation t = 3w models your total savings

Use your equation to find out how much money will be saved after 15 weeks by plugging in 15 for w.

T = 3(15) = $45

Example 2: You buy CD’s from a music store. Each CD costs $15. Make a table and write an equation to represent the total cost of buying a given number of CD’s. How much would it cost to buy 12?

Number of CD’s

purchased (n)

Cost

(c)

Expression

C = 15n

0 0

1 15

2 30

15(0)

15(1)

15(2)

-You need to choose a variable to represent number of CD’s purchased and cost. Then write an equation.

The equation C = 15n models your total cost for purchasing n CD’s

Use your equation to find out how much it will cost to purchase 12 CD’s by plugging in 12 for N.

C = 15(12) = $180

-When you graph linear equations plug in 2 numbers for x and see what you get out as your y. Then plot the points on a coordinate plane.

Example 3: Graph each linear equation below by picking two values for x and seeing what you get out as your y. Make a table and then plot your points.

a.) y = 5x – 2 b.) y = -1/2x + 4

x y

0

1

x y

0

1

-2

3

4

3.5

Now plot the points and draw the line

Now plot the points and draw the line

Example 4: Determine whether each ordered pair below is a solution to the equation y = 3x – 8

a.) (0,-8) b.) (-2, 2) c.) (4, 4)

Y = 3(0) – 8Y = 0 – 8Y = -8

Yes

Y = 3(-2) -8Y = -6 – 8Y= -14

No

Y = 3(4) -8Y = 12 – 8Y= 4

Yes

Example 5: Art Application

An engraver charges a setup fee of $10 plus $2 for every word engraved. Write a rule for the engraver’s fee. Write ordered pairs for the engraver’s fee when there are 5, 10, 15, and 20 words engraved.

Let y represent the engraver’s fee and x represent the number of words engraved.

EngraverEngraver’’s fees fee isis $10$10 plusplus $2$2 for eachfor each wordword

yy == 1010 ++ 22 ·· xx

y = 10 + 2x

The engraver’s fee is determined by the number of words in the engraving. So the number of words is the input and the engraver’s fee is the output.

Writing MathWriting Math

Example 5 Continued

Number ofWords

EngravedRule Charges

Ordered Pair

x (input) y = 10 + 2x y (output) (x, y)

y = 10 + 2(5)5 20 (5, 20)

y = 10 + 2(10)10 30 (10, 30)

y = 10 + 2(15)15 40 (15, 40)

y = 10 + 2(20)20 50 (20, 50)

Check It Out! Example 6

What if…? The caricature artist increased his fees. He now charges a $10 set up fee plus $20 for each person in the picture. Write a rule for the artist’s new fee. Find the artist’s fee when there are 1, 2, 3 and 4 people in the picture.

y = 10 + 20x

Let y represent the artist’s fee and x represent the number of people in the picture.

Artist’s fee is $10 plus $20 for each person

y = 10 + 20 · x

Number of People in Picture

Rule ChargesOrdered

Pair

x (input) y = 10 + 20x y (output) (x, y)

y = 10 + 20(1)1 30 (1, 30)

y = 10 + 20(2)2 50 (2, 50)

y = 10 + 20(3)3 70 (3, 70)

y = 10 + 20(4)4 90 (4, 90)

Check It Out! Example 6 Continued

When you graph ordered pairs generated by a function, they may create a pattern.

Example 7A: Generating and Graphing Ordered Pairs Generate ordered pairs for the function using the given values for x. Graph the ordered pairs and describe the pattern.

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The points form a line.

y = 2x + 1; x = –2, –1, 0, 1, 2

–2–1012

2(–2) + 1 = –3 (–2, –3)(–1, –1)(0, 1)(1, 3)(2, 5)

2(–1) + 1 = –12(0) + 1 = 12(1) + 1 = 32(2) + 1 = 5

Input OutputOrdered

Pairx y (x, y)

HomeworkHomeworkPg 132 Pg 132

##5-8 all 5-8 all - make a table and write and - make a table and write and equationequation

#10-12 all #10-12 all – write down three – write down three coordinates and create the line on graph coordinates and create the line on graph paperpaper

Example 7B: Generating and Graphing Ordered Pairs

y = x2 – 3; x = –2, –1, 0, 1, 2

–2

–10

1

2

(–2)2 – 3 = 1 (–2, 1)

(–1, –2)(0, –3)

(1, –2)

(2, 1)

(–1)2 – 3 = –2(0)2 – 3 = –3

(1)2 – 3 = –2(2)2 – 3 = 1

Input OutputOrdered

Pairx y (x, y)

The points form a U shape.

Example 7C: Generating and Graphing Ordered Pairs

y = |x – 2|; x = 0, 1, 2, 3, 4

0

12

3

4

|0 – 2| = 2 (0, 2)

(1, 1)(2, 0)

(3, 1)

(4, 2)

|1 – 2| = 1|2 – 2| = 0

|3 – 2| = 1

|4 – 2| = 2

Input OutputOrdered

Pairx y (x, y)

The points form a V shape.

Homework Quiz

1.) A cable company charges $50 to set up 1.) A cable company charges $50 to set up a movie channel and $3.00 per movie a movie channel and $3.00 per movie watched. Write a rule for the company’s watched. Write a rule for the company’s fee. Write ordered pairs for the fee when fee. Write ordered pairs for the fee when a person watches 1, 2, 3, or 4 movies.a person watches 1, 2, 3, or 4 movies.

y = y = 50 + 350 + 3x; x; (1, 53), (2, 56), (3, 59), (4, 62)(1, 53), (2, 56), (3, 59), (4, 62)