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Graphing Linear Equations

Starting with an x/y table. Graphing Linear Equations. Warm-up. 1. Find the slope by counting. 2. Determine the slope of the line formed by ( -3, 14) and (-3,-9). Answer : m = undefined. Answer: m = -1/2 . How do you solve this equation?. 2x – 3 = 17. + 3 +3. 2 2.

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Graphing Linear Equations

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  1. Starting with an x/y table Graphing Linear Equations

  2. Warm-up 1. Find the slope by counting 2. Determine the slope of the line formed by ( -3, 14) and (-3,-9) Answer: m = undefined Answer: m = -1/2

  3. How do you solve this equation? 2x – 3 = 17 + 3 +3 2 2 2x = 20 x = 10 What is a major difference between the equation above and 2x – y = 17? Because the equations now have 2 variables, the solutions will come in pairs…ordered pairs (x, y)

  4. Let’s see how to determine if an ordered pair IS a solution… Each linear equation will have an infinite amount of solutions that come in pairs. (x,y)

  5. EXAMPLE 1: ON GRAPHIC ORGANIZER Determine if each ordered pair is a solution to the equation y = 4x – 1. A. (3,11) (x, y) y = 4x – 1 Use the substitution property to plug in the values of x and y. 11 = 4(3) - 1 11 = 12 - 1 Conclusion: Yes, (3, 11) is a solution because it falls on the line, y = 4x - 1 11 = 11

  6. EXAMPLE 1: ON GRAPHIC ORGANIZER Determine if each ordered pair is a solution to the equation y = 4x – 1. B. (10,3) (x, y) y = 4x – 1 Use the substitution property to plug in the values of x and y. 3 = 4(10) - 1 3 = 40 - 1 Conclusion: No, (10, 3) is a not a solution. It does not fall on the line, y = 4x - 1 3 = 39

  7. EXAMPLE 1: ON GRAPHIC ORGANIZER Determine if each ordered pair is a solution to the equation y = 4x – 1. C. (11, 43) Try this one on your own! Conclusion: Yes, ( 11, 43) is a solution. It falls on the line, y = 4x – 1.

  8. What do all the solutions to a linear equation look like? They form a line in the coordinate plane!

  9. Example 2: Graph 4x – 3y = 6 1st: Solve the equation for y 4x – 3y = 6 -4x - 4x – 3y = -4x + 6 -3 -3 y = 4/3x -2

  10. Example 2: Graph 4x – 3y = 6 X is independent. Choose any number for x and plug it into the equation 2 (3,2) In this problem, it’s smart to choose multiples of 3 since you must multiply by 4/3. 0 -2 (0,-2) -3 -6 (-3,-6) 6 6 (6,6)

  11. Plot your four points • These are only 4 solutions. Since there are an infinite amount of solutions, draw a line through the points. Every point that falls on the line is a solution. Label your line Make sure your line has arrows!

  12. Example 3: Graph x + 2 = 0 • This equation doesn’t have a y. Therefore, isolate x . Choose any values for y • x + 2 = 0 • - 2 -2 • x = -2 • -4 • 0 • 1 • 5 X is fixed at -2

  13. Example 3: Graph & Label line Rule of thumb: Draw your line as big as your coordinate plane. No little , itty -bitty lines in a huge plane! x= -2

  14. Example 4: Graph y = -3 • Do this on your own! (click for answer) y = -3

  15. Begin Homework • Graph paper is located in my supply closet. (Double cabinets closest to the classroom door.) • Page 351 Oral exercises #1-12, • Page 357 #29-36 all • If you have a graphing calculator, bring it to class tomorrow.

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