Graph y>=x+3 y<=2x-6

$y \geq x + 3$ $y \leq 2 x - 6$

Step 1

Graph $y \geq x + 3$ .

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 2

Graph $y \leq 2 x - 6$ .

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 $y = m x + b$ .

$m = 2$

$b = - 6$

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

Slope: $2$

y-intercept: $(0, - 6)$

Slope: $2$

y-intercept: $(0, - 6)$

Graph a solid line, then shade the area below the boundary line since $y$ is less than $2 x - 6$ .

$y \leq 2 x - 6$

Step 3

Plot each graph on the same coordinate system.

$y \geq x + 3$

$y \leq 2 x - 6$

Step 4