Jordan uses a linear equation to model the data in a table. Which reasoning might Jordan have used in the decision to model the data with a linear equation?
The products of corresponding x- and y-values are equal.
The ratios of consecutive y-values are equal for evenly spaced x-values.
The change in y-values is not constant, but the change is constant for evenly spaced x-values.
The change in y-values is constant for evenly spaced x-values.
slope = change in y / change in x
the change in y will not be constant unless you pick evenly spaced x values (the same changes in x)
if change in y is constant for evenly spaced x values then the slope is constant so it is a straight line.
helkop
The reasoning that Jordan might have used in the decision to model the data with a linear equation is that the change in y-values is constant for evenly spaced x-values.
Jordan might have used the reasoning that the change in y-values is constant for evenly spaced x-values.
To determine whether a linear equation is a good model for the data, one should examine the pattern or trend in the data. If the change in y-values is consistent or constant (i.e., the difference between consecutive y-values is the same), and this pattern holds for evenly spaced intervals of x-values, then a linear equation is a suitable model.
By examining the data, if the increase or decrease in y-values is constant for equally spaced x-values, it suggests a linear relationship. This means that for every unit increase or decrease in x, there is a constant change in the corresponding y-value. This consistent change in y-values indicates a linear relationship and justifies the decision to model the data with a linear equation.