Question

finding the rate of change from a table
examine the table and determine the rate of change.
what is the rate of change?
options: -4, -3, 1, 3
table:

x	y
2	-1
3	2
4	5

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 given by \(\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Select two points from the table

Let's take the first two points: \((x_1, y_1) = (1, -4)\) and \((x_2, y_2) = (2, -1)\).

Step3: Calculate the rate of change

Substitute into the formula: \(\frac{-1 - (-4)}{2 - 1} = \frac{-1 + 4}{1} = \frac{3}{1} = 3\)? Wait, no, wait. Wait, let's check another pair. Wait, maybe I picked wrong points. Wait, let's take \((2, -1)\) and \((3, 2)\). Then \(\frac{2 - (-1)}{3 - 2} = \frac{3}{1} = 3\). Wait, or \((1, -4)\) and \((2, -1)\): \(\frac{-1 - (-4)}{2 - 1} = \frac{3}{1} = 3\). Wait, but let's check the options. Wait, the options are -4, -3, 1, 3. Wait, maybe I made a mistake. Wait, no, wait the table: when x=1, y=-4; x=2, y=-1; x=3, y=2; x=4, y=5. So the change in y from x=1 to x=2: -1 - (-4) = 3. Change in x: 2 - 1 = 1. So rate of change is 3. Wait, but let's check again. Wait, maybe the user made a typo? Wait, no, the table: x=1, y=-4; x=2, y=-1 (so y increases by 3 when x increases by 1). x=2 to x=3: y goes from -1 to 2, increase by 3. x=3 to x=4: 2 to 5, increase by 3. So rate of change is 3.

Answer:

3 (corresponding to the option with 3, e.g., if the options are as given, the correct one is the option with 3, like D. 3 if options are A. -4, B. -3, C. 1, D. 3)