How do you find the area of the region bounded by the two axes and the line y=4-3x?

Sep 15, 2015

$\frac{8}{3}$

Explanation:

graph{4-3x}

It's a triangle with 90 degree angle, so $p = \frac{a b}{2}$; intersection of the given line with y-axis is $a$ and with x-axis is $b$.
$x = 0 , y = 4 \implies a = 4$
$y = 0 , 0 = 4 - 3 x , x = \frac{4}{3} \implies b = \frac{4}{3}$
$P = \frac{4 \cdot \frac{4}{3}}{2} = \frac{8}{3}$