Equation of the line passing through the point (5$$,$$4) and making an angle $$45$$∘ with negative direction of x $$-$$ axis is

Question

Equation of the line passing through the point (5$$,$$4) and making an angle $$45$$∘ with  negative direction of x $$-$$ axis is

Infinity Learn · Accepted Answer

Equation of line passing through the point $$x1$$,$$y1$$ and having slope m is y−$$y1=mx$$−$$x1$$ Here $$m=$$$$tan$$⁡θ, where θ is angle made by the line with x $$-$$ axis in the positive direction.  Since the line making an angle $$45$$∘ with negative direction of x $$-$$ axis, the angle made by the  line with positive direction of x− axis is $$180$$∘−$$45$$∘$$=135$$∘ Hence the slope of the line is $$m=$$$$tan$$⁡$$135$$∘$$=$$−$$1$$ The equation of the line passing through the point (5$$,$$4) and having slope −$$1$$ is y−$$4=$$−$$(x$$−$$5)y$$−$$4=$$−$$x+5x+y$$−$$9=0$$ Therefore, the equation of the line is $$x+y$$−$$9=0$$

$Equation of the line passing through the point (5, 4) and making an angle 45^{\circ} with$ $negative direction of x - axis is$

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Equation of the line passing through the point (5,4) and making an angle 45∘ with negative direction of x - axis is

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$Equation of the line passing through the point (5, 4) and making an angle 45^{\circ} with$ $negative direction of x - axis is$