<u>Given </u><u>:</u><u>-</u>
- A equation which is 5x - 2y = 7 .
<u>To </u><u>Find</u><u> </u><u>:</u><u>-</u>
- The equation of the line perpendicular to the given line and passes through (3,-2) .
<u>Solution</u><u> </u><u>:</u><u>-</u>
Given equation to us is ,
Convert it into slope intercept form which is y = mx + c ,
Divide both sides by 2 ,
Now on comparing to slope intercept form , we have ,
And as we know that the product of slopes of two perpendicular lines is -1 . Therefore the slope of the perpendicular line will be negative reciprocal of slope of the given line . As ,
Again the given point to us is (3,-2) . We may use the point slope form to find out the equation of perpendicular line which is ,
Substitute ,
Open the brackets and simplify,
Subtracting 2 both sides ,
Simplify,
![\longrightarrow \underline{\underline{ y = \dfrac{-2}{5}x -\dfrac{4}{5}}}](https://tex.z-dn.net/?f=%5Clongrightarrow%20%5Cunderline%7B%5Cunderline%7B%20y%20%3D%20%5Cdfrac%7B-2%7D%7B5%7Dx%20-%5Cdfrac%7B4%7D%7B5%7D%7D%7D)
This is the required answer !