Question

At a glance, Kendra believes that the function represented on the graph is linear.

How can Kendra determine if the function is actually linear?

She can check to see if the rate of vertical increase equals the rate of horizontal increase between each pair of points.
She can check to see if the sum of each y-value and x-value in every ordered pair is the same.
She can check to see if the quotient of each y-value and x-value in every ordered pair is the same.
She can check to see if the rate of change between the first two ordered pairs is the same as the rate of change between the first and last ordered pairs.

Answer 1

Correct choice: "She can check to see if the rate of change between the first two ordered pairs is the same as the rate of change between the first and last ordered pairs."

Reason: a function is linear exactly when the slope (rise/run) is the same between any two pairs of points. So compute slope = (change in y)/(change in x) for the first two points and for the first and last points — if those slopes are equal (and likewise for any other pairs), the points lie on a straight line.

Why the others are wrong:
- Checking x+y constant tests only for lines with slope −1, not all lines.
- Checking y/x constant tests only for lines through the origin (proportional relationships).
- The first option, as written, is ambiguous; the correct test uses the quotient (change in y)/(change in x) being constant, not that the vertical and horizontal "rates" are equal.