Question

Robin always finds at least three different ordered pairs when making a table to graph an equation. Why do you think she does this?

Short answer

Robin uses at least three different ordered pairs when graphing an equation to check that the points lie on the same line or form a consistent pattern, leading to a more accurate representation of the function.

Step-by-step solution

Understanding the concept of graphing an equation

To graph an equation, one needs to represent it visually using a set of points in a two-dimensional plane. Each point corresponds to an ordered pair \((x, y)\), where \(x\) is the input value and \(y\) is the corresponding output value from the equation.

The Role of Multiple Points

By plotting multiple points, one can get a better understanding of the shape and nature of the graph. The minimum requirement of points to define a straight line graph is two, but in practice graphing only two points may not be sufficient to accurately depict the behavior of the function, particularly if it's not linear.

The Reasoning Behind Three Points

By plotting a minimum of three points, Robin is ensuring the accuracy of her graph. Three points allow for validation that the points lie on the same line (for linear functions) or form a consistent pattern (for non-linear functions). The third point acts as a confirmation of the trend suggested by the first two points.