Answer:
The slope of a line that is perpendicular to the given line is [tex]-\frac{3}{2}[/tex]
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
Solve for "y" from the equation of the line [tex]2x - 3y - 5 = 0[/tex]:
[tex]2x - 3y - 5 = 0\\\\-3y=-2x+5\\\\y=\frac{-2}{-3}x+\frac{5}{-3}\\\\y=\frac{2}{3}x-\frac{5}{3}[/tex]
You can observe that the slope of this line is:
[tex]m=\frac{2}{3}[/tex]
By definition, the slopes of perpendicular lines are negative reciprocal, then, the slope of a line that is perpendicular to the give line, is
[tex]m=-\frac{3}{2}[/tex]
