Question

graphing an inequality in two variables
graph ( y < \frac{1}{3}x + \frac{1}{2} )
which point is a solution to the inequality?
( circ (-2, 1) )
( circ (-1, 1) )
( circ left(0, \frac{1}{2}
ight) )
( circ left(3, \frac{1}{2}
ight) )
the correct line is shown

Explanation:

Step1: Substitute (-2,1) into inequality

$1 < \frac{1}{3}(-2) + \frac{1}{3}$
$1 < \frac{-2+1}{3}$
$1 < -\frac{1}{3}$ (False)

Step2: Substitute (-1,1) into inequality

$1 < \frac{1}{3}(-1) + \frac{1}{3}$
$1 < \frac{-1+1}{3}$
$1 < 0$ (False)

Step3: Substitute $(0,\frac{1}{2})$ into inequality

$\frac{1}{2} < \frac{1}{3}(0) + \frac{1}{3}$
$\frac{1}{2} < \frac{1}{3}$ (False, since $\frac{1}{2}>\frac{1}{3}$)

Step4: Substitute $(3,\frac{1}{2})$ into inequality

$\frac{1}{2} < \frac{1}{3}(3) + \frac{1}{3}$
$\frac{1}{2} < 1 + \frac{1}{3}$
$\frac{1}{2} < \frac{4}{3}$ (True)

Answer:

(3, $\frac{1}{2}$)