Graph y<=-x+4 , y>=x+2 , y>=0 , x>=0

$y \leq - x + 4$ , $y \geq x + 2$ , $y \geq 0$ , $x \geq 0$

Step 1

Graph $y \leq - x + 4$ .

Use the slope-intercept form to find the slope and y-intercept.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = - 1$

$b = 4$

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $- 1$

y-intercept: $(0, 4)$

Slope: $- 1$

y-intercept: $(0, 4)$

Graph a solid line, then shade the area below the boundary line since $y$ is less than $- x + 4$ .

$y \leq - x + 4$

Step 2

Graph $y \geq x + 2$ .

Use the slope-intercept form to find the slope and y-intercept.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = 1$

$b = 2$

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $1$

y-intercept: $(0, 2)$

Slope: $1$

y-intercept: $(0, 2)$

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $x + 2$ .

$y \geq x + 2$

Step 3

Graph $y \geq 0$ .

$y \geq 0$

Step 4

Graph $x \geq 0$ .

$x \geq 0$

Step 5

Plot each graph on the same coordinate system.

$y \leq - x + 4$

$y \geq x + 2$

$y \geq 0$

$x \geq 0$

Step 6