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# Find the equations of the straight lines which cut off an intercept 5 from the y - axis and are equally inclined to the axes.

Last updated date: 18th Mar 2023
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Hint:  Whenever there is written equally inclined on the axes and a point through which lines pass is given then the best way is to find the equation of line using point - slope form..

As it is given that lines cut off an intercept of 5 on y - axis and equally inclined on both axes.

And as we know that x - axis and y - axis are always inclined at $90^\circ$

So, $\angle PQO = \angle OPQ = \angle PRO = \angle OPR = {45^\circ }$

So, as we see from the above figure that we have to find the equation of lines PQ and PR.

As we know point P is known and is (0,5)

Finding equation of line PQ,

$\Rightarrow$ Slope of line PQ will be $\tan \left( {135} \right) = - 1$

$\Rightarrow$ So, equation of line PQ with point slope form will be,

$\Rightarrow (y - 5) = - 1\left( {x - 0} \right){\text{ }} \Rightarrow y = 5 - x$ (Equation of line PQ)

Finding equation of line PR,

$\Rightarrow$ Slope of line PR will be $\tan \left( {45} \right) = 1$

$\Rightarrow$ So, the equation of line PR with point slope form will be.

$\Rightarrow \left( {y - 5} \right) = 1\left( {x - 0} \right){\text{ }} \Rightarrow y = 5 + x{\text{ }}$ (Equation of line PR)

Hence equations of lines that cut off an intercept 5 from y - axis and equally inclined on axes will be,

$\Rightarrow y = 5 \pm x$

Note: Understand the diagram properly whenever you are facing these kinds of problems. A better knowledge of formulas will be an added advantage.