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=-\frac{1}{m_2}$$m_1=-3$$\begin{gathered} -3=-\frac{1}{m_2} \\ m_2=-\frac{1}{-3} \\ m_2=\frac{1}{3} \end{gathered}$

Step 2

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

Find b, the y-intercept

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

Answer; Option D

$y=\frac{1}{3}x+1$