Question

What is the equation of the line perpendicular to `y=27/12x` that passes through `(2,1)`?

Answer 1

suppose,the equation of the line required is `y=mx +c`

Now,slope of the given equation `y=(27/12)x` is `27/12=9/4`

If, our required straight line needs to be perpendicular on the given staright line,then we can say, `m.(9/4) =-1`

So, `m=-(4/9)`

So,we found the slope of our line,hence we can put it and write as,

`y=(-4x)/9 +c`

Now,given that this line passes through the point `(2,1)`

So,we can put the value to determine the intercept,

so, `1=(-4*2)/9 +c`

or, `c=17/9`

So,the equation of our line becomes, `y=(-4x)/9 +17/9` or, `9y+4x=17 graph{9y+4x=17 [-10, 10, -5, 5]}`