A graph includes the ordered pair (2, 4). Write two different rules that would be possible for this graph. Explain how you found your answer.

Two potential rules for the ordered pair (2,4) on a graph are y = x + 2 and y = 2x, both satisfying the condition when x = 2, yielding the y-value of 4.
Given an ordered pair (2,4), we can establish multiple mathematical rules that would place this pair on their respective graph. Two possible rules are:

y = x + 2
y = 2x

To determine these rules, we use the x-value of the ordered pair to generate an equation that would yield the y-value when solved. For example, if x is 2, the rule y = x + 2 would give us y = 2 + 2, which equals 4. Similarly, the rule y = 2x would lead to y = 2 × 2, which is also 4.
Therefore, both equations satisfactorily include the given ordered pair (2,4) on their graph.

Answered by ToddBoyce | 2024-06-24

Two possible rules for the ordered pair (2, 4) are y = x + 2 and y = 2x. Both rules give the y-value of 4 when x is 2. This shows how different functions can share the same point in a graph.
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Answered by ToddBoyce | 2024-12-23