Question

look at this table:

x	y
3	16
4	20
5	24
6	28
7	32

write a linear ($y = mx + b$), quadratic ($y = ax^2$), or exponential ($y = a(b)^x$) function that models the data.
$y = \boxed{}$

Explanation:

Step1: Calculate slope $m$

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{20 - 16}{4 - 3} = 4$

Step2: Find y-intercept $b$

Substitute $x=3, y=16, m=4$ into $y=mx+b$:
$16 = 4(3) + b$
$16 = 12 + b$
$b = 16 - 12 = 4$

Step3: Verify linear fit

Check with $x=5$: $y=4(5)+4=24$, matches the table.
Check with $x=7$: $y=4(7)+4=32$, matches the table.

Answer:

$y = 4x + 4$