Question

Is the relationship shown in the table linear? Explain.
−1 5
2 -4
7 -19
10 -28

Yes, the rate of change is not constant between ordered pairs.

No, the rate of change is constant between all ordered pairs.

Yes, the rate of change is constant between all ordered pairs.

No, the rate of change is not constant between ordered pairs.

Answer 1

Yes — the rate of change is constant between all ordered pairs.

Compute slopes:
- Between (-1, 5) and (2, -4): (−4 − 5)/(2 − (−1)) = −9/3 = −3
- Between (2, −4) and (7, −19): (−19 − (−4))/(7 − 2) = −15/5 = −3
- Between (7, −19) and (10, −28): (−28 − (−19))/(10 − 7) = −9/3 = −3

All slopes are −3, so the relationship is linear (equation y = −3x + 2).