The symbols <, >, $\leq$, $\geq$ denote inequalities.

Graph the region for the linear inequality y $\leq$ -2x + 3

The given equation represents Slope-Intercept form with m = -2 and c = 3

We can solve for the given points algebraically

using the slope formula.

$\frac{y_{2} - y_{1}}{x_{2}-x_{1}}$ = m

Plug in $x_{2}$ = 0 and $y_{2}$ = 3 ($y_{1}$ = y, $x_{1}$ = x)

$\frac{3 - y}{0 - x}$ =

$\frac{-2}{1}$

3 - y = -2

$\Rightarrow$ y = 5

and -x = 1

$\Rightarrow$ x = -1

So now we have the point (-1, 5)

To find another point plug in $y_{1}$ = -3 and $x_{1}$ = 0

($y_{2}$ = y, $x_{2}$ = x) we get

$\frac{y -3}{x - 0}$ =

$\frac{-2}{1}$

y - 3 = -2 $\Rightarrow$ y = 1

x - 0 = 1 $\Rightarrow$ x = 1

The other point is (1, 1) .

**Given below is the graph for the given equation:**From the graph we see the points are same so the answer is verified.

**The shaded region gives the solution to the given problem**.