Question

line j is perpendicular to lines m and n. if the products of the slope of all three lines is -8, what is the slope of line j?

Answer 1

the slope of line j is -1/8, the slope of lines m and n are both 8.

Explanation step by step:

Suppose j is the slope of line j, m the slope of line m and n the slope of line n. Since:

1. line j is perpendicular of line m, so j*m= -1

2. J is perpendicular of line n, so j*n=-1

3. m and n and parallel so m=n

As we want to know the slope of j we clear the equations presented to us in order to find it.

(1) m* n* j = -8, since n=m we have
`n^(2)`* j = -8.

we clear j;
`n^(2) * j = -8 \\ j =(-8)/(n^(2) )`

replacing in the equation n*j = -1 we get

n*(-8/n^2) = -1. Thus n = 8. Since j = -1/n = -1/8.