Question

1. write an algebraic equation for the following table:

$x$

$y$

----

----

3

13

5

21

9

37

11

45

Explanation:

Step1: Identify slope (rate of change)

First, calculate the slope $m$ using two points, e.g., $(3,13)$ and $(5,21)$:
$$m=\frac{21-13}{5-3}=\frac{8}{2}=4$$

Step2: Find y-intercept $b$

Use slope-intercept form $y=mx+b$, substitute $m=4$ and point $(3,13)$:
$$13=4(3)+b$$
$$13=12+b$$
$$b=13-12=1$$

Step3: Verify with other points

Check $(9,37)$: $y=4(9)+1=36+1=37$, which matches. Check $(11,45)$: $y=4(11)+1=44+1=45$, which matches.

Answer:

$y=4x+1$