Question

Which of the following equations represents a line that is perpendicular toy=-3x+6 and passes through the point, (3, 2)?A. y=-3x+1B. y=(1/3x)+3C. y=(-1/3x)+1OD. y=(1/3x)+1

Answer 1

Step 1

For perpendicular lines

`m_1=-(1)/(m_2)`
`m_1=-3`
`\begin{gathered} -3=-(1)/(m_2) \\ m_2=-(1)/(-3) \\ m_2=(1)/(3) \end{gathered}`

Step 2

`\begin{gathered} Given\text{ points \lparen3,2\rparen} \\ y=mx+b---\text{ Standard equation of a line} \\ y=(1)/(3)x+b \end{gathered}`
`2=(1)/(3)(3)+b`

Find b, the y-intercept

`\begin{gathered} 2=1+b \\ b=2-1=1 \end{gathered}`

Answer; Option D

`y=(1)/(3)x+1`