Q7. Find the equation of the straight line passing through line passing through the point (4,...

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Q7. Find the equation of the straight line passing through line passing through the point (4, 5) and the sum of its intercepts on the axes is 18. Q7. Find the equation of the straight line passing through line passing through the point (4, 5) and the sum of its intercepts on the axes is 18.

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To find the equation of the straight line passing through the point 4 5 and the sum of its intercepts on the axes is 18 we can follow these steps Let the xintercept be a and the yintercept be b Given that the sum of the intercepts is 18 we have a b 18 1 Now the formula for the equation of a line passing through the point x1 y1 with intercepts a and b is xa yb 1 Substitute the given point 4 5 into the equation to get 4a 5b 1 2 From equations 1 and 2 we have a system of two equations in two variables Solving these equations simultaneously will give us the values of a and b which in turn will help us determine the equation of the straight line Lets solve these equations to find the intercepts a and b first From equation 1 we have a b 18 b 18 a 3 Substitute the value of b from equation 3 into equation 2 4a 518 a 1 Multiplying by a18 a to clear the denominators 418 a 5a a18 a 72 4a 5a 18a a2 72 a a2 18a Rearranging the terms a2 17a 72 0 a 24a 3 0 Therefore the intercepts are a 24 or a 3 Since the intercept ... View the full answer