Graph y<=-x-1 y>=5/2x-8

$y \leq - x - 1$ $y \geq \frac{5}{2} x - 8$

Step 1

Graph $y \leq - x - 1$ .

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 $y = m x + b$ .

$m = - 1$

$b = - 1$

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

Slope: $- 1$

y-intercept: $(0, - 1)$

Slope: $- 1$

y-intercept: $(0, - 1)$

Graph a solid line, then shade the area below the boundary line since $y$ is less than $- x - 1$ .

$y \leq - x - 1$

Step 2

Graph $y \geq \frac{5}{2} x - 8$ .

Find the slope and the y-intercept for the boundary line.

Rewrite in slope-intercept form.

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

$y = m x + b$

Simplify the right side.

Combine $\frac{5}{2}$ and $x$ .

$y \geq \frac{5 x}{2} - 8$

Reorder terms.

$y \geq \frac{5}{2} x - 8$

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

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

$m = \frac{5}{2}$

$b = - 8$

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

Slope: $\frac{5}{2}$

y-intercept: $(0, - 8)$

Slope: $\frac{5}{2}$

y-intercept: $(0, - 8)$

Slope: $\frac{5}{2}$

y-intercept: $(0, - 8)$

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $\frac{5}{2} x - 8$ .

$y \geq \frac{5}{2} x - 8$

Step 3

Plot each graph on the same coordinate system.

$y \leq - x - 1$

$y \geq \frac{5}{2} x - 8$

Step 4