Graph y<=x y>=3-x

$y \leq x$ $y \geq 3 - x$

Step 1

Graph $y \leq x$ .

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 $y = m x + b$ .

$m = 1$

$b = 0$

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

Slope: $1$

y-intercept: $(0, 0)$

Slope: $1$

y-intercept: $(0, 0)$

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

$y \leq x$

Step 2

Graph $y \geq 3 - x$ .

Reorder $3$ and $- x$ .

$y \geq - x + 3$

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 $y = m x + b$ .

$m = - 1$

$b = 3$

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

Slope: $- 1$

y-intercept: $(0, 3)$

Slope: $- 1$

y-intercept: $(0, 3)$

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $- x + 3$ .

$y \geq - x + 3$

Step 3

Plot each graph on the same coordinate system.

$y \leq x$

$y \geq 3 - x$

Step 4