Question

Given the line 2x - 3y - 5 = 0, find the slope of a line that is perpendicular to this line.

Answer 1

Answer:  

The slope of a line that is perpendicular to the given line is $-\frac{3}{2}$

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope of the line and "b" is the y-intercept.

Solve for "y" from the equation of the line $2x - 3y - 5 = 0$:

$2x - 3y - 5 = 0\\\\-3y=-2x+5\\\\y=\frac{-2}{-3}x+\frac{5}{-3}\\\\y=\frac{2}{3}x-\frac{5}{3}$

You can observe that the slope of this line is:

$m=\frac{2}{3}$

By definition, the slopes of perpendicular lines are negative reciprocal, then, the slope of a line that is perpendicular to the give line, is

$m=-\frac{3}{2}$