Let's do this question, find the equation of the line that makes zero intercept on X and Y axis and
is perpendicular to the line five X plus eight Y minus nine is equal to zero.
All right, let's get started.
Over here, let's take Y is equal to a mix policy.
All right, now it's mentioned over here that the intercept on the X and Y axis is zero, right?
That means this line passes through the origin and hence C over here is equal to zero.
Right now.
A line can have zero X and Y intercept when it passes through the origin.
Right.
This is an example of a line that passes through the origin.
That is zero zero is part of the line.
Now, why does it not have and Y or X intercept when it passes to the origin?
Let's quickly see that as a side note.
Let the equation of the line be wise and mix policy.
Now, if zero zero is on this line, let me substitute it over here so I get zero is equal to amount
to zero plus C, right.
So zero equals zero policy and C also has to be equal to zero.
All right.
Now we have seen that the given line passes through the origin and hence the equation of the line is
Y is equal to imex.
Now it's mentioned that it's perpendicular to the line five X plus eight Y minus nine is equal to zero.
Right.
Let me write it like this.
Eight Y is equal to minus five X plus nine.
Now let me change it into the form Y is equal to a mix policy to Y is equal to minus five by eight X
plus nine by it.
Right.
So what is the slope of the given line.
It's minus five by eight.
Right.
This is the slope.
Now if this line over here has to be perpendicular to this line, then the slope should be such that
when you multiply the two slopes, you should get minus one.
Therefore, the slope over here is equal to eight by five.
Right.
And that's because eight by five in the minus, five by eight is equal to minus one.
And hence the equation of this line is Y is equal to eight by five X.
That is our answer.
Right.
And this can also be written five Y minus eight X is equal to zero.
Now, quickly, let's revise.
We have the line given us eight Y plus five X minus nine is equal to zero.
If we want to directly write a line that is perpendicular to this line or we need to do is we need to
exchange the coefficients and we need to change the sign.
Right.
So it becomes five Y minus.
Eight X plus C is equal to zero, right, and C will be based on the Y intercept.
And in this case, because it passes through the origin, C will be equal to zero and you get five Y
minus eight, X is equal to zero, which is the same thing that we got over here.