Question

find the equation of a line perpendicular to y -9= 2/3(x-3) that passes through the point (6,1) in slope intercept form

Answer 1

The Solution.

The given equation is

`y-9=(2)/(3)(x-3)`

To determine the slope of the line, we shall express the equation in the y =mx + c , where m is the slope.

`\begin{gathered} y-9=(2)/(3)(x-3) \\ \text{Clearing the bracket, we get} \\ y-9=(2)/(3)x-2 \\ \text{Collecting the like terms, we get} \\ y=(2)/(3)x-2+9 \\ \\ y=(2)/(3)x+7 \end{gathered}`

The slope of the given equation is 2/3.

But to obtain the slope a line that is perpendicular to the given line, we use the formula below:

`m_2=-(1)/(m_1)`