Question

What is the slope of a line perpendicular to the line whose equation is102 + 6y = -84. Fully simplify

Answer 1

Given data:

The given equation is 10x+6y= -84.

The given equation can be written as,

`\begin{gathered} 6y=-10x-84 \\ y=-(10)/(6)x-(84)/(6) \\ =-(5)/(3)x-14 \end{gathered}`

The standard equation of the line is,

`y=mx+c`

Compare both the equations.

`m=-(5)/(3)`

The expression for the slope perpendicular to the given line is,

`\begin{gathered} m^(\prime)=-(1)/(m) \\ m^(\prime)=-(1)/((-(5)/(3))) \\ =(3)/(5) \end{gathered}`

Thus, the slope of the line perpendicular to the given line is 3/5.