Graph y>=3/4x+5 y<-5/2x-8

$y \geq \frac{3}{4} x + 5$ $y < - \frac{5}{2} x - 8$

Step 1

Graph $y \geq \frac{3}{4} x + 5$ .

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 $\frac{3}{4}$ and $x$ .

$y \geq \frac{3 x}{4} + 5$

Reorder terms.

$y \geq \frac{3}{4} x + 5$

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

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

$m = \frac{3}{4}$

$b = 5$

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

Slope: $\frac{3}{4}$

y-intercept: $(0, 5)$

Slope: $\frac{3}{4}$

y-intercept: $(0, 5)$

Slope: $\frac{3}{4}$

y-intercept: $(0, 5)$

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $\frac{3}{4} x + 5$ .

$y \geq \frac{3}{4} x + 5$

Step 2

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

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.

Simplify each term.

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

$y < - \frac{x \cdot 5}{2} - 8$

Move $5$ to the left of $x$ .

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

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

Reorder terms.

$y < - (\frac{5}{2} x) - 8$

Remove parentheses.

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

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 dashed line, then shade the area below the boundary line since $y$ is less than $- \frac{5}{2} x - 8$ .

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

Step 3

Plot each graph on the same coordinate system.

$y \geq \frac{3}{4} x + 5$

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

Step 4

Graph y>=3/4x+5 y<-5/2x-8

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