Question

1. write an algebraic equation for the following table:

Explanation:

Step1: Check linear relationship

First, calculate the slope between two points, e.g., $(8,8)$ and $(11,14)$:
$\text{slope } m = \frac{14-8}{11-8} = \frac{6}{3} = 2$
Verify with another pair, e.g., $(3,-2)$ and $(5,2)$:
$m = \frac{2-(-2)}{5-3} = \frac{4}{2} = 2$
The slope is constant, so it's linear.

Step2: Find y-intercept $b$

Use the slope-intercept form $y = mx + b$, substitute $m=2$, and point $(8,8)$:
$8 = 2(8) + b$
$8 = 16 + b$
$b = 8 - 16 = -8$

Step3: Build the equation

Substitute $m=2$ and $b=-8$ into $y=mx+b$.

Answer:

$y = 2x - 8$