Question

find the linear function that is the best fit for the data.

x	y
3	2
5	3
7	4
9	5

what is the linear function of the data?
( y = square x + (square) )
(type integers or decimals.)

Explanation:

Step1: Identify slope pattern

Notice that for each increase of $x$ by 2, $y$ increases by 1. So slope $m=\frac{\Delta y}{\Delta x}=\frac{1}{2}=0.5$.

Step2: Verify with point (1,1)

Use linear form $y=mx+b$. Substitute $x=1,y=1,m=0.5$:
$1 = 0.5(1) + b$
Solve for $b$: $b=1-0.5=0.5$

Step3: Confirm with other points

Check $x=3$: $y=0.5(3)+0.5=2$, which matches the table.
Check $x=5$: $y=0.5(5)+0.5=3$, which matches the table.

Answer:

$y=0.5x + 0.5$