Question

what is the constant rate of change in the given table?
x | y
0 | 17
1 | 14
2 | 11
3 | 8

Explanation:

Step1: Recall rate of change formula

The rate of change (slope) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Pick two consecutive points

Take \((0, 17)\) and \((1, 14)\). Here, \(x_1 = 0\), \(y_1 = 17\), \(x_2 = 1\), \(y_2 = 14\).

Step3: Calculate rate of change

Substitute into the formula: \(\frac{14 - 17}{1 - 0}=\frac{-3}{1}=-3\).
Check with another pair, e.g., \((1,14)\) and \((2,11)\): \(\frac{11 - 14}{2 - 1}=\frac{-3}{1}=-3\). Consistent.

Answer:

-3