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**Homework Statement**

A straight line L with negative slope passes through the point (8,2) and cuts the positive coordinate axes at points P and Q. As L varies, what is the absolute minimum value of OP + OQ?

**The attempt at a solution**

Let x and y be two points on the line.

Using the slope point formula, we have (y-2) = m(x-8).

Writing this in intercept form, one gets x/(8 - 2/m) + y/(2 - 8m) = 1.

This implies coordinates of P and Q are (8 - 2/m, 0) and (0, 2 - 8m) respectively.

∴ OP + OQ = 10 + (-2/m - 8/m)

I can't figure out how to proceed from there. How do you find out the minimum value for the last term?