Question

1. several students made statements about the relationship between x and y shown in the table. circle the name of any student who made a correct statement. tabitha the relationship is non - linear because as x increases, y decreases. arturo the relationship is non - linear because as x changes by a constant value, the y - values do not change by a constant value. luke a graph of the relationship would not show a straight line. 4. select the name of any student who made a correct statement. tabitha arturo luke

Explanation:

Step1: Analyze Tabitha's statement

A linear relationship can also have \(y\) decreasing as \(x\) increases (e.g., \(y=-x\)). So, Tabitha's statement is incorrect.

Step2: Analyze Arturo's statement

For a linear relationship, if \(x\) changes by a constant value (\(\Delta x\)), \(y\) changes by a constant value (\(\Delta y\)). Here, when \(x\) changes by \(2\) (from \(0\) to \(2\), \(2\) to \(4\), \(4\) to \(6\)), \(y\) changes by \(- 4\) (from \(0\) to \(-4\)), then by \(-12\) (from \(-4\) to \(-16\)), then by \(-20\) (from \(-16\) to \(-36\)). Since \(\Delta y\) is not constant, the relationship is non - linear. Arturo's statement is correct.

Step3: Analyze Luke's statement

A linear relationship has a graph that is a straight line. Since the relationship is non - linear (from Arturo's analysis), a graph of the relationship would not show a straight line. Luke's statement is correct.

Answer:

Arturo, Luke