Question

which table could be a partial set of values for a linear function?

x	y
1	5
2	7
3	9

x	y
1	8
2	5
3	0

Explanation:

Step1: Recall linear function property

A linear function has a constant rate of change (slope), calculated as $\frac{\Delta y}{\Delta x}$ between consecutive points.

Step2: Analyze left table

• From \(x = 0\) to \(x = 1\): \(\Delta y=5 - 3 = 2\), \(\Delta x = 1-0 = 1\), slope \(=\frac{2}{1}=2\).
• From \(x = 1\) to \(x = 2\): \(\Delta y=7 - 5 = 2\), \(\Delta x = 2 - 1 = 1\), slope \(=\frac{2}{1}=2\).
• From \(x = 2\) to \(x = 3\): \(\Delta y=9 - 7 = 2\), \(\Delta x = 3 - 2 = 1\), slope \(=\frac{2}{1}=2\). Slope is constant.

Step3: Analyze right table

• From \(x = 0\) to \(x = 1\): \(\Delta y=8 - 9=-1\), \(\Delta x = 1-0 = 1\), slope \(=-1\).
• From \(x = 1\) to \(x = 2\): \(\Delta y=5 - 8=-3\), \(\Delta x = 2 - 1 = 1\), slope \(=-3\). Slope is not constant.

Answer:

The table on the Left (with \(x\) values 0,1,2,3 and \(y\) values 3,5,7,9)