Question

what is the graph

of the inequality
$12y \leqslant 16x$

Answer 1

$12y\leq16x\qquad|\text{divide both sides by 12}\\\\y\leq\dfrac{16}{12}x\\\\y\leq\dfrac{16:4}{12:4}x\\\\y\leq\dfrac{4}{3}x\\--------------------------\\\\y=\dfrac{4}{3}x\\\\for\ x=0\to y=\dfrac{4}{3}(0)=0\to(0,\ 0)\\\\for\ x=3\to y=\dfrac{4}{3}(3)=4\to(3,\ 4)\\\\\text{we shade below the line}$