Table of Values
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Question 1 of 5
1. Question
Complete the following table given the equation`y=3x+1``x` `0` `1` `2` `y` Hint
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A table of values is used to find the ordered pairs `(``x``,``y``)` of points on a lineStart by working out the `\text(y-values)` for each `\text(x-value)` in the table of values.`x` `0` `1` `2` `y` Substitute `x=0` into the given equation.`y` `=` `3``x``+1` `=` `3(``0``)+1` Substitute the value of `x` `=` `0+1` Simplify `y` `=` `1` `x` `0` `1` `2` `y` `1` Substitute `x=1` into the given equation.`y` `=` `3``x``+1` `=` `3(``1``)+1` Substitute the value of `x` `=` `3+1` Simplify `y` `=` `4` `x` `0` `1` `2` `y` `1` `4` Substitute `x=2` into the given equation.`y` `=` `3``x``+1` `=` `3(``2``)+1` Substitute the value of `x` `=` `6+1` Simplify `y` `=` `7` `x` `0` `1` `2` `y` `1` `4` `7` `x` `0` `1` `2` `y` `1` `4` `7` -
Question 2 of 5
2. Question
List the ordered pairs for `y=5x-3``x` `0` `1` `2` `y` Hint
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A table of values is used to find the ordered pairs `(``x``,``y``)` of points on a lineStart by working out the `\text(y-values)` for each `\text(x-value)` in the table of values.`x` `0` `1` `2` `y` Substitute `x=0` into the given equation.`y` `=` `5(``0``)-3` Substitute the value of `x` `=` `0-3` Simplify `y` `=` `-3` `x` `0` `1` `2` `y` `-3` Substitute `x=1` into the given equation.`y` `=` `5``x``-3` `=` `5(``1``)-3` Substitute the value of `x` `=` `5-3` Simplify `y` `=` `2` `x` `0` `1` `2` `y` `-3` `2` Substitute `x=2` into the given equation.`y` `=` `5``x``-3` `=` `5(``2``)-3` Substitute the value of `x` `=` `10-3` Simplify `y` `=` `7` `x` `0` `1` `2` `y` `-3` `2` `7` Write the coordinates from the table.`(0,-3), (1,2)` and `(2,7)``(0,-3), (1,2)` and `(2,7)` -
Question 3 of 5
3. Question
Find the formula for the following table of values.`x` `1` `2` `3` `4` `5` `y` `3` `7` `11` `15` `19` Hint
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A table of values is used to find the `x` and `y` ordered pairs of points on a lineFind the multiplier from the difference of consecutive `y` values.`7-3` `=` `4` `11-7` `=` `4` `15-11` `=` `4` `19-15` `=` `4` Multiplier is `4` Write a formula with the multiplier `(4)` and let `b` be the constant.`y=``4``x +-` `b`Slot in a given ordered pair to find the value of the constant `b`Use the ordered pair `(``1``,``3``)` from the table of values`y` `=` `4``x``+``b` `3` `=` `4``(1)``+``b` If `x=1`, `y=3` `3` `=` `4+``b` `-1` `=` `b` Subtract `4` from both sides `b` `=` `-1` The formula can be written as:`y` `=` `4x-``1` Check our workLets check if our formula is correct by plugging in a `\text(x-value)` from the table into the formulaCheck the value of `y`, when `x=2` from the table`y` `=` `4``x``-1` `=` `4``(2)``-1` Plug in `x=2` `=` `8-1` Simplify `y` `=` `7` `y=7` when `x=2` matches the table `x` `1` `2` `3` `4` `5` `y` `3` `7` `11` `15` `19` `y=4x-1` -
Question 4 of 5
4. Question
Find the formula for the following table of values.`x` `1` `2` `3` `4` `5` `y` `-3` `-1` `1` `3` `5` Hint
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A table of values is used to find the `x` and `y` ordered pairs of points on a lineFind the multiplier from the difference of consecutive `y` values.`-1-(-3)` `=` `2` `1-(-1)` `=` `2` `3-1` `=` `2` `5-3` `=` `2` Multiplier is `2` Write a formula with the multiplier `(2)` and let `b` be the constant.`y=``2``x +-` `b`Slot in a given ordered pair to find the value of the constant `b`Use the ordered pair `(``1``,``-3``)` from the table of values`y` `=` `2``x``+``b` `-3` `=` `2``(1)``+``b` If `x=1`, `y=-3` `-3` `=` `2+``b` `-5` `=` `b` Subtract `2` from both sides `b` `=` `-5` The formula can be written as:`y` `=` `2x-``5` Check our workLets check if our formula is correct by plugging in a `\text(x-value)` from the table into the formulaCheck the value of `y`, when `x=2` from the table`y` `=` `2``x``-5` `=` `2``(2)``-5` Plug in `x=2` `=` `4-1` Simplify `y` `=` `-1` `y=-1` when `x=2` matches the table `x` `1` `2` `3` `4` `5` `y` `-3` `-1` `1` `3` `5` `y=2x-5` -
Question 5 of 5
5. Question
Find the formula for the following table of values.`f` `0` `1` `2` `3` `4` `m` `-2` `1` `4` `7` `10` Hint
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A table of values is used to find the `x` and `y` ordered pairs of points on a lineFind the multiplier from the difference of consecutive `m` values.`1-(-2)` `=` `3` `4-1` `=` `3` `7-4` `=` `3` `10-7` `=` `3` Multiplier is `3` Write a formula with the multiplier `(3)` and let `b` be the constant.`m=``3``f +-` `b`Slot in a given ordered pair to find the value of the constant `b`Use the ordered pair `(``0``,``-2``)` from the table of values`m` `=` `3``f``+``b` `-2` `=` `3``(0)``+``b` If `f=0`, `m=-2` `-2` `=` `0+``b` `-2` `=` `b` Simplify `b` `=` `-2` The formula can be written as:`m` `=` `3f-``2` Check our workLets check if our formula is correct by plugging in a `\text(x-value)` from the table into the formulaCheck the value of `m`, when `f=2` from the table`m` `=` `3``f``-2` `=` `3``(2)``-2` Plug in `f=2` `=` `6-2` Simplify `m` `=` `4` `m=4` when `f=2` matches the table `f` `0` `1` `2` `3` `4` `m` `-2` `1` `4` `7` `10` `m=3f-2`