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!
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!
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.