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Looking for Rules in a Table Finding a Linear Rule from a table The general Linear Equation is y = mx + c m c = the constant (gradient) = the y -intercept Example One x y -2 1 -1 2 0 3 1 4 2 5 3 6 Step One: Check to see if our top row is in order from smallest to largest. If not create a new table and arrange in order Step Two: Find the difference the x values are going up or down by. (arrows on table above) Step Three: Find the difference the y values are going up or down by.(arrows on table above) Step Four: To find the Constant multiplier (gradient) we take the y value difference and divide it by the x value difference. Step Five: Now we need to fond the y-intercept a) we can look at the column where x = 0 and find the corresponding y-value. This is the y-intercept b) If we don’t have x = 0 we can choose a point to substitute in to find the c value (y-intercept Example Two: a b -3 -4 Example Three: t w 2 -3 Example Four: p m -4 4 Find the rule from the table -2 -1 -1 2 0 5 1 8 2 11 5 0 6 1 7 2 2 -8 4 -12 Find the rule from the table 3 -2 4 -1 Find the rule from the table -2 0 0 -4 Finding a Quadratic Rule from a table 2 y = ax + bx + c The general Quadratic Equation is a = half of the second difference c = the y –intercept b is found using substitution Example One x y -2 5 -1 2 0 1 1 2 2 5 3 10 Step One: Check to see if our top row is in order from smallest to largest. If not create a new table and arrange in order Step Two: Find the first difference the y values are going up or down by. (arrows on table above) Step Three: If the first deifference are not the same then the equation is not linear. Now do a second difference. Step Four: If the second difference is the same then it is a quadratic equation. Step Five: The a value is half of this second difference. Step Six: Determine the c value. This is the y value when x = 0 in our table. Step Seven: Choose a point to substitute into our equation to find our b value. Example Two: a b -3 8 Example Three: t w 2 5 Example Four: x y -2 15 Find the rule from the table -2 4 -1 2 0 2 1 4 2 8 5 29 6 41 7 54 1 0 2 -1 Find the rule from the table 3 11 4 19 Find the rule from the table -1 8 0 3 For all of the tables below: Find if there is any relationship or pattern If there is a pattern what type of graph is it Linear or Quadratic or neither If there is a linear or quadratic graph what is the equation of that graph x y 1 -31 2 -28 3 -25 4 -22 5 -19 6 -16 7 -13 8 -10 9 -7 x y 1 12 2 6 3 4 4 3 5 2.4 6 2 7 1.71 8 1.5 9 1.33 x y -3 14 -2 9 -1 6 0 5 1 6 9 3 14 x y 4 4 5 6 6 8 7 10 8 12 9 14 10 16 2 11 18 x y -5 4 -4 9 x y -4 -16 x y 1 4 2 6 3 8 6 14 7 16 x y 2 5 3 13 4 23 5 35 6 49 -3 -9 -3 16 -2 -4 -2 25 -1 -1 -1 36 0 0 0 49 1 1 7 65 1 64 2 4 2 81