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Let's do this question, find the equation of the line that makes zero intercept on X and Y axis and

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is perpendicular to the line five X plus eight Y minus nine is equal to zero.

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All right, let's get started.

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Over here, let's take Y is equal to a mix policy.

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All right, now it's mentioned over here that the intercept on the X and Y axis is zero, right?

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That means this line passes through the origin and hence C over here is equal to zero.

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Right now.

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A line can have zero X and Y intercept when it passes through the origin.

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Right.

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This is an example of a line that passes through the origin.

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That is zero zero is part of the line.

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Now, why does it not have and Y or X intercept when it passes to the origin?

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Let's quickly see that as a side note.

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Let the equation of the line be wise and mix policy.

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Now, if zero zero is on this line, let me substitute it over here so I get zero is equal to amount

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to zero plus C, right.

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So zero equals zero policy and C also has to be equal to zero.

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All right.

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Now we have seen that the given line passes through the origin and hence the equation of the line is

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Y is equal to imex.

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Now it's mentioned that it's perpendicular to the line five X plus eight Y minus nine is equal to zero.

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Right.

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Let me write it like this.

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Eight Y is equal to minus five X plus nine.

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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

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plus nine by it.

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Right.

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So what is the slope of the given line.

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It's minus five by eight.

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Right.

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This is the slope.

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Now if this line over here has to be perpendicular to this line, then the slope should be such that

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when you multiply the two slopes, you should get minus one.

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Therefore, the slope over here is equal to eight by five.

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Right.

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And that's because eight by five in the minus, five by eight is equal to minus one.

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And hence the equation of this line is Y is equal to eight by five X.

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That is our answer.

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Right.

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And this can also be written five Y minus eight X is equal to zero.

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Now, quickly, let's revise.

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We have the line given us eight Y plus five X minus nine is equal to zero.

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If we want to directly write a line that is perpendicular to this line or we need to do is we need to

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exchange the coefficients and we need to change the sign.

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Right.

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So it becomes five Y minus.

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Eight X plus C is equal to zero, right, and C will be based on the Y intercept.

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And in this case, because it passes through the origin, C will be equal to zero and you get five Y

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minus eight, X is equal to zero, which is the same thing that we got over here.