1 / 23

Go over homework

Go over homework. 3-5 Equations, Tables, and Graphs. 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 – 8 Because -8 = 3(0) -8

ezra
Download Presentation

Go over homework

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Go over homework

  2. 3-5 Equations, Tables, and Graphs

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

  4. Linear Equation • • • if all of its solutions lie on a line • • Curvy line Straight line Continuous line

  5. 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. Input Output y= 10x + 5 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.

  6. 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? -You need to choose a variable to represent number of weeks and total savings. Then write an expression. w t 3(w) 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

  7. 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? -You need to choose a variable to represent number of CD’s purchased and cost. Then write an expression. 15(0) 15(1) 15(2) N C 15(N) 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

  8. -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 Now plot the points and draw the line Now plot the points and draw the line -2 4 3 3.5

  9. 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) – 8 Y = 0 – 8 Y = -8 Yes Y = 3(-2) -8 Y = -6 – 8 Y= -14 No Y = 3(4) -8 Y = 12 – 8 Y= 4 Yes

  10. Engraver’s fee is $10 plus word $2 for each y 10 x = + 2 · 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. y = 10 + 2x

  11. Writing Math 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.

  12. Example 5 Continued 5 y = 10 + 2(5) 20 (5, 20) 10 30 (10, 30) y = 10 + 2(10) y = 10 + 2(15) 15 (15, 40) 40 20 50 y = 10 + 2(20) (20, 50)

  13. Artist’s fee is $10 plus person $20 for each y 10 x = + 20 · 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. Let y represent the artist’s fee and x represent the number of people in the picture. y = 10 + 20x

  14. Check It Out! Example 6 Continued 1 y = 10 + 20(1) 30 (1, 30) 2 50 (2, 50) y = 10 + 20(2) y = 10 + 20(3) 3 (3, 70) 70 4 90 y = 10 + 20(4) (4, 90)

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

  16. • • • • • 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. y = 2x + 1; x = –2, –1, 0, 1, 2 (–2, –3) –2 2(–2)+ 1 = –3 2(–1)+ 1 = –1 (–1, –1) –1 2(0)+ 1 = 1 (0, 1) 0 2(1) + 1 = 3 1 (1, 3) 2(2) + 1 = 5 (2, 5) 2 The points form a line.

  17. Homework Pg 132 #5-8 all - make a table and write and equation #10-12 all – write down three coordinates and create the line on graph paper

  18. Example 7B: Generating and Graphing Ordered Pairs y = x2– 3; x = –2, –1, 0, 1, 2 (–2, 1) –2 (–2)2– 3 = 1 (–1)2– 3 = –2 –1 (–1, –2) (0)2– 3 = –3 (0, –3) 0 (1)2– 3 = –2 1 (1, –2) (2)2– 3 = 1 (2, 1) 2 The points form a U shape.

  19. Example 7C: Generating and Graphing Ordered Pairs y = |x –2|; x = 0, 1, 2, 3, 4 0 (0, 2) |0– 2| = 2 |1– 2| = 1 1 (1, 1) |2– 2| = 0 (2, 0) 2 |3– 2| = 1 3 (3, 1) (4, 2) 4 |4– 2| = 2 The points form a V shape.

  20. Homework Quiz 1.) A cable company charges $50 to set up a movie channel and $3.00 per movie watched. Write a rule for the company’s fee. Write ordered pairs for the fee when a person watches 1, 2, 3, or 4 movies. y = 50 + 3x; (1, 53), (2, 56), (3, 59), (4, 62)

More Related