Question

Please help me solve the problem and identify what the error was in solving it

Answer 1

To answer this question, we must noted that:

The slopes of two perpendicular lines are negative reciprocals of each other:

`\begin{gathered} m_1m_2=-1 \\ \text{Where } \\ m_1\text{ is the slope of one of the lines} \\ m_2\text{ is the slope of the line perpendicular to the other line} \end{gathered}`

First, we will find what the slope of the initial equation is:

`\begin{gathered} 10x-8y=-80 \\ 10x+80=8y \\ (10x)/(8)+(80)/(8)=(8y)/(8) \\ (5)/(4)x+10=y \end{gathered}`

So from the above solution, we see that:

`m_1=(5)/(4)`

We will solve for the slope of a line perpendicular to it thus:

`\begin{gathered} m_1m_2=-1 \\ (5)/(4)m_2=-1 \end{gathered}`

Simplifying further:

`\begin{gathered} m_2=-(1)/((5)/(4)) \\ =-1/(5)/(4) \\ =-1*(4)/(5) \\ =(-4)/(5) \\ \text{The slope of a line perpendicular to the line with equation 10x-8y=-80 is:} \\ (-4)/(5) \end{gathered}`