Question

Find the equation of the line that goes through the point ( 3, 1 ) and is perpendicular to the line y = -3/2x + 32.

Answer 1

`y=(2)/(3)x-1\:`

Explanation:

The equation in its slope-intercept form is as follows:

`\begin{gathered} y=mx+b \\ \\ \text{ where m is the slope and b is y-intercept} \end{gathered}`

We can calculate the slope since we know the slope of a perpendicular line, when the slopes are perpendicular the product of the slopes is equal to -1, therefore:

`\begin{gathered} m_1\cdot m_2=-1 \\ \\ -(3)/(2)\cdot m_2=-1 \\ \\ m_2=(2)/(3) \end{gathered}`

Now, we calculate the y-intercept with the slope and the point (3, 1), like this:

`\begin{gathered} 1=(2)/(3)\cdot3+b \\ \\ 1=2+b \\ \\ b=-2+1 \\ \\ b=-1 \end{gathered}`

So the equation would be:

`y=(2)/(3)x-1\:`