Hey, I need some help with a problem

determine the equation of the straight line passing through (1,3) and together with the coordinate axes forms a triangle with the smallest possible area.

Not sure how to think about all this.

Thanks!

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- Nov 11th 2012, 05:30 AMYahikkoEquation of a line problem
Hey, I need some help with a problem

determine the equation of the straight line passing through (1,3) and together with the coordinate axes forms a triangle with the smallest possible area.

Not sure how to think about all this.

Thanks! - Nov 11th 2012, 06:26 AMrichard1234Re: Equation of a line problem
I'm assuming the triangle has to be in the first quadrant? Because it's possible to construct a triangle of area zero in the 2nd and 4th quadrants.

Suppose the equation of the line, in slope-intercept form, is

$\displaystyle y - 3 = m(x - 1)$

$\displaystyle y = mx + (3-m)$

Here, the y-intercept is 3-m (where m < 0), and you can solve for the x-intercept. Once you find the x-intercept, find the area in terms of m, and minimize it.