Question

1. write an algebraic equation for the following table:

x	y
4	15
6	21
11	36

Explanation:

Step1: Find slope $m$

Take two points $(x_1,y_1)=(1,6)$ and $(x_2,y_2)=(4,15)$.
$m=\frac{y_2-y_1}{x_2-x_1}=\frac{15-6}{4-1}=\frac{9}{3}=3$

Step2: Solve for y-intercept $b$

Use $y=mx+b$, substitute $m=3$, $x=1$, $y=6$.
$6=3(1)+b \implies b=6-3=3$

Step3: Verify equation

Check $(6,21)$: $y=3(6)+3=21$, matches. Check $(11,36)$: $y=3(11)+3=36$, matches.

Answer:

$y=3x+3$