Question

function 1 is defined by the following table.
r y
0 2
1 1.5
2 1
3 0.5

Explanation:

Step1: Identify the pattern

Looking at the table, when \( r \) increases by 1 (from 0 to 1, 1 to 2, 2 to 3), \( y \) decreases by 0.5 (from 2 to 1.5, 1.5 to 1, 1 to 0.5). So the slope \( m \) is \( \frac{\Delta y}{\Delta r}=\frac{-0.5}{1} = - 0.5\) or \(-\frac{1}{2}\). When \( r = 0\), \( y = 2\), so the y - intercept \( b=2\).

Step2: Write the linear function

The slope - intercept form of a linear function is \( y=mx + b\). Substituting \( m=-\frac{1}{2}\) and \( b = 2\), we get \( y=-\frac{1}{2}r + 2\).

Answer:

The linear function representing the table is \( y =-\frac{1}{2}r + 2\)