Answer :
To calculate the perpendicular slope, the steps are the following:
• Step 1: Find the original slope of the line
,• Step 2: Use the condition for the perpendicular slope, to find the perpendicular slope.
Step 1. To find the slope of the given line
[tex]y=\frac{8}{3}x-4[/tex]we need to compare this with the slope-intercept equation
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept of the line. Thus, we can see that the number that accompanies the x represents the slope. And in this line
[tex]y=\frac{8}{3}x-4[/tex]That number is 8/3. I will call this the slope m1:
[tex]m_1=\frac{8}{3}[/tex]Step 2. The condition for two lines m1 and m2 to be perpendicular is:
[tex]m_1\times m_2=-1[/tex]Since in this case we know the original slope m1, and we are looking for perpendicular slope m2, we substitute m1, and solve for m2:
[tex]\frac{8}{3}\times m_2=-1[/tex]Solving for m2, we need to multiply each side of the equation by 3/8:
[tex]\frac{3}{8}\times\frac{8}{3}\times m_2=-1\times\frac{3}{8}[/tex]On the left side we are only left with m2, and on the right side we are left with -3/8:
[tex]m_2=-\frac{3}{8}[/tex]Answer: -3/8