Question

Determine the equation of the line that passes through the point (1/8,2) and is perpendicular to the line 5y+2x=2.

Answer 1

Step 1

Given;

Determine the equation of the line that passes through the point (1/8,2) and is perpendicular to the line 5y+2x=2.

Step 2

Find the slope of the new line based on a perpendicular relationship

`\begin{gathered} m_1=-(1)/(m_2) \\ \end{gathered}`
`\begin{gathered} 5y=2-2x \\ y=(2-2x)/(5) \\ y=(2)/(5)-(2)/(5)x \\ -(2)/(5)=-(1)/(m_2) \\ 2m_2=5 \\ m_2=(5)/(2) \end{gathered}`

Thus the equation will be;

`\begin{gathered} ((1)/(8),2) \\ y=(5)/(2)x+b \\ b=y-intercept \\ 2=(5)/(2)((1)/(8))+b \\ 2=(5)/(16)+b \\ b=2-(5)/(16) \\ b=(27)/(16) \end{gathered}`
`y=(5)/(2)x+(27)/(16)`

Answer;

`y=(5)/(2)x+(27)/(16)`