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Equations Tables and Graphs

Equations Tables and Graphs. These are all connected to each other. They all show the same information but in different forms. Equation y = 6x + 8 Table x y Ordered pair ( x,y ) Graph Slope. Straight Lines. When given an equation and told to plot a graph, first find

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Equations Tables and Graphs

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  1. Equations Tables and Graphs

  2. These are all connected to each other. They all show the same information but in different forms • Equation y = 6x + 8 • Table x y • Ordered pair (x,y) • Graph • Slope

  3. Straight Lines When given an equation and told to plot a graph, first find coordinates of points on the line, this is done by completing a table. By substituting the given values for x calculate the y value for the following equation: y = x + 2 -1 0 1 3 5 2 4 This generates coordinates to plot on a graph (-3,-1) (0, 2) (1, 3) (-2,0) (-1, 1) (2, 4) (0, 2) (3, 5)

  4. y 10 9 8 7 6 5 4 3 2 1 x 0 -10 1 2 3 4 5 6 7 9 10 -9 -8 -6 -4 -3 -2 8 -7 -5 -1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 Plotting these points Straight Lines (-3,-1) (0, 2) (1, 3) (-2,0) (-1, 1) (2, 4) (0, 2) (3, 5) x x x x x x We find a straight line x x

  5. y 10 9 8 7 6 5 4 3 2 1 x 0 -10 1 2 3 4 5 6 7 9 10 -9 -8 -6 -4 -3 -2 8 -7 -5 -1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 Straight Lines Copy and complete this table for the following equation and plot the straight line x y = 3x - 1 -10 -1 2 8 -4 x x x x

  6. Worksheet 1 y 10 9 8 7 6 5 4 3 2 1 x 0 -10 1 2 3 4 5 6 7 9 10 -9 -8 -6 -4 -3 -2 8 -7 -5 -1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 Complete the table for the equation y = x Straight Lines Plot the coordinates When the table is completed Complete the table for the equation y = x +1 Complete the table for the equation y = x + 3 Complete the table for the equation y = x - 2

  7. What do I do if I don’t have the points given to me??? • y = 2x+ 2

  8. Graphing Step 1: ~ Five Point Method ~ Choose 5 values for x

  9. Graphing Step 2: Find solutions using table y = x + 3 Y | X 0 1 2

  10. Graphing Step 3: Graph the points from the table (0,3) (1,4) (2,5)

  11. Graphing Step 4: Draw a line to connect them

  12. Linear Equations:Equation of a straight line Standard form is AX + BY = C

  13. Slope-Intercept y = mx + b m = slope b = y-intercept

  14. Slope Describes the steepness of a line or rate of change

  15. Y-intercept Where the line crosses the y-axis

  16. Y-intercept The y-intercept has an x-coordinate of ZERO

  17. Y-intercept To find the y-intercept, plug in ZERO for x and solve

  18. X-intercept Where the line crosses the x-axis

  19. X-intercept The x-intercept has a y coordinate of ZERO

  20. X-intercept To find the x-intercept, plug in ZERO for y and solve

  21. Try These • Graph using a table (5 point method) 1) y = x + 3 2) y = x - 4

  22. Equation: X Y

  23. A phone company charges $17.50 per month and 12 c for each additional minute . Write a linear equation for the charge in terms of the number of minutes. Let C = charge in dollars Let m =# of minutes C = 17.50 + 0.12 m Start Value Change

  24. This chart shows the price of sliced fruit platters. 1) How much would a 6 lb. platter cost? $8.10 + 1.50 = $ 9.60 1.50 1.50 2) Write an equation for the cost of a platter that weighs w lbs. 1.50 1.50 Let p = price of platter 3) How much would a 10 lb. platter cost? p = 1.50 w + 0.60 p = 1.50 w + 0.60 Change Start Value p = 1.50 ( 10 ) + 0.60 p = 15.00 + 0.60 = $15.60

  25. Y = 0.75X + 3 • You are visiting Baltimore, MD, and a taxi company charges the flat fee of $3.00 for using the taxi and an additional &0.75 per mile. Write an equation that you could use to find the cost of a taxi ride in Baltimore, MD. Let X represent the number of miles and Y represent the total cost.

  26. Kim and Cyndi are starting a business tutoring students in math. They rent an office for $100 per week and charge $40 per hour per student.  If they have 15 students each for one hour per week how much profit do they make together in a week? Write and equation.

  27. Suppose that the water level of a river is 34 feet and that it is receding at a rate of 0.5 foot per day. Write an equation for the water level, L, after d days. In how many days will the water level be 26 feet?

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