Question

write the linear equation that gives the rule for this table.

x | y
3 | 9
4 | 12
5 | 15
6 | 18

write your answer as an equation with y first, followed by an equals sign.

Explanation:

Step1: Calculate slope (rate of change)

Choose two points, e.g., $(3,9)$ and $(4,12)$.
Slope $m = \frac{12-9}{4-3} = 3$

Step2: Verify slope consistency

Check with $(5,15)$ and $(6,18)$:
$m = \frac{18-15}{6-5} = 3$

Step3: Find y-intercept $b$

Use $y=mx+b$, substitute $x=3, y=9, m=3$:
$9 = 3(3) + b$
$9 = 9 + b$
$b = 0$

Step4: Form linear equation

Substitute $m=3, b=0$ into $y=mx+b$

Answer:

$y = 3x$