Graph x+y<=5 x+y<=4 x>=0 y>=0

$x + y \leq 5$ $x + y \leq 4$ $x \geq 0$ $y \geq 0$

Step 1

Graph $x + y \leq 5$ .

Write in $y = m x + b$ form.

Subtract $x$ from both sides of the inequality.

$y \leq 5 - x$

Rearrange terms.

$y \leq - x + 5$

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 $y = m x + b$ .

$m = - 1$

$b = 5$

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

Slope: $- 1$

y-intercept: $(0, 5)$

Slope: $- 1$

y-intercept: $(0, 5)$

Graph a solid line, then shade the area below the boundary line since $y$ is less than $- x + 5$ .

$y \leq - x + 5$

Step 2

Graph $x + y \leq 4$ .

Write in $y = m x + b$ form.

Subtract $x$ from both sides of the inequality.

$y \leq 4 - x$

Rearrange terms.

$y \leq - x + 4$

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 3

Graph $x \geq 0$ .

$x \geq 0$

Step 4

Graph $y \geq 0$ .

$y \geq 0$

Step 5

Plot each graph on the same coordinate system.

$x + y \leq 5$

$x + y \leq 4$

$x \geq 0$

$y \geq 0$

Step 6

Graph x+y<=5 x+y<=4 x>=0 y>=0

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