Question

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

x	y
3	11
5	16
7	21
9	26

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

Explanation:

Step1: Calculate slope $m$

The data is perfectly linear, so use $\text{slope} = \frac{\Delta y}{\Delta x}$. Take $(x_1,y_1)=(1,6)$ and $(x_2,y_2)=(3,11)$:
$$m = \frac{11-6}{3-1} = \frac{5}{2} = 2.5$$

Step2: Calculate y-intercept $b$

Use $y = mx + b$, substitute $x=1, y=6, m=2.5$:
$$6 = 2.5(1) + b$$
Solve for $b$:
$$b = 6 - 2.5 = 3.5$$

Step3: Form linear function

Substitute $m$ and $b$ into $y=mx+b$.

Answer:

$y=2.5x+(3.5)$