# Thread: Equation of a line problem

1. ## Equation 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!

2. ## Re: 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.