Answer:
[tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Hi there!
In the given equation, [tex]y= -\frac{2}{3} x -5[/tex], the slope of the line is [tex]-\frac{2}{3}[/tex].
Perpendicular lines always have slopes that are negative reciprocals, like negative "flipped" fractions.
Example: The reciprocal of [tex]\frac{2}{1}[/tex] (which is the same as 2) is [tex]\frac{1}{2}[/tex]. The negative of [tex]\frac{1}{2}[/tex] is [tex]-\frac{1}{2}[/tex].
Example 2: The negative reciprocal of [tex]-\frac{4}{3}[/tex] is [tex]\frac{3}{4}[/tex].
Using this logic, we can determine that the negative reciprocal of [tex]-\frac{2}{3}[/tex] is [tex]\frac{3}{2}[/tex]. Therefore, the slope of a line perpendicular to the line whose equation is [tex]y= -\frac{2}{3} x -5[/tex] would be [tex]\frac{3}{2}[/tex].
I hope this helps!
