Find the point on the line 4x + y = 7 that is closest to the point (-5, 2). (Give your answers correct to two decimal places.)
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Are you using calculus to solve this or can you use something else?
If calculus, then best idea is to use the distance formula. The points on the line will be (x, 7-4x) and the distance between any point on the line and (-5,2) is (x+5)^2 + (7-4x-2)^2 or more simply (x+5)^2+ (5-4x)^2. Expand carefully and you will get a quadratic in x. To find the minimum value, take the derivative, set it = 0 and solve, or just use -b/2a. that will give you the x coordinate of the minimum value, and the y you find by substitution.
ok then that method should work. You have the square of the distance, not the distance, but that is ok. when you expand you get 17x^2-30x+50. Call this f(x) and your derivative is 34x - 30, which is zero when x is 15/17. Makes an ugly decimal which is probably why they asked for two decimal places.