Question

Find the equation of the line that is perpendicular to 2x-9y=-3 and also goes through the point (-1, 2). Write the answer in slope intercept form

Answer 1

`y=-(9)/(2)x-(5)/(2)`

Step-by-step explanation

Two lines are perpendicular if their slopes are opposite reciprocals of each other.

In this case, we can rewrite the equation of the given line in slope-intercept form by solving the equation for y,

`2x-9y=-3`

Add 9y to both sides,

`\begin{gathered} 2x-9y+9y=-3+9y \\ 2x=-3+9y \end{gathered}`

Add 3 to both sides,

`2x+3=9y`

And divide both sides by 9,

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

As we can see, the slope of the given line is 2/9. Its opposite reciprocal is -9/2. This is the slope of the line we have to find,

`y=-(9)/(2)x+b`

To find the y-intercept, b, we have to use the point (-1, 2). Replace x and y with the coordinates of the point,

`2=-(9)/(2)(-1)+b`

And solve for b,

`\begin{gathered} 2=(9)/(2)+b \\ \\ 2-(9)/(2)=b \\ \\ (4-9)/(2)=b \\ \\ -(5)/(2)=b \end{gathered}`

Hence, the equation of the line is,

`y=-(9)/(2)x-(5)/(2)`