Question

1. consider this table:

x	1	2	3	4
y	9	10	11	12

enter an equation that represents the relationship shown in the table.

Explanation:

Step1: Identify linear relationship

Check $\Delta y$ and $\Delta x$:
$\Delta x = 2-1=1$, $\Delta y=10-9=1$; $\Delta x=3-2=1$, $\Delta y=11-10=1$. Slope $m=\frac{\Delta y}{\Delta x}=1$.

Step2: Find y-intercept b

Use $x=1, y=9$ in $y=mx+b$:
$9=1\times1+b$
$b=9-1=8$

Step3: Write the equation

Substitute $m=1, b=8$ into slope-intercept form.

Answer:

$y = x + 8$