Give the perpendicular slope of the given line y=8/3x-4

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