Question

which ordered pair does not fall on the line formed by the other three? *
(16, 18)
(12, 12)
(9, 10)
(3, 6)

Explanation:

Step1: Find slope between (3,6) & (9,10)

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{10-6}{9-3}=\frac{4}{6}=\frac{2}{3}$

Step2: Write line equation (point-slope)

Use point (3,6): $y-y_1=m(x-x_1)$
$y-6=\frac{2}{3}(x-3)$
Simplify: $y=\frac{2}{3}x + 4$

Step3: Test (12,12) in equation

Substitute $x=12$: $y=\frac{2}{3}(12)+4=8+4=12$ (matches)

Step4: Test (16,18) in equation

Substitute $x=16$: $y=\frac{2}{3}(16)+4=\frac{32}{3}+4=\frac{44}{3}\approx14.67$ (≠18)

Answer:

(16, 18)