Question

A line passes through the points shown in this table. What is the slope of a line perpendicular to this line?

x	1	3	5	7
y	2	5	8	11

• A. 3/2
• B. -2/3
• C. -3/2
• D. 2/3

Answer 1

The correct option is B -2/3

Slope of a line for given any two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by

$\frac{y_2-y_1}{x_2-x_1}$

From the table, taking any two points gives us the slope as $\frac{3}{2}$

For example, at $(1,2)$ and $(3,5)$
Slope $=\frac{5-2}{3-1}=\frac{3}{2}$

OR at $(3,5)$ and $(5,8)$, slope $=\frac{8-5}{5-3}=\frac{3}{2}$

If two lines are perpendicular, their slopes are negative reciprocals.

$\therefore$ A perpendicular has a slope of $-\frac{2}{3}$.