Graph y>=3/2x-3 y<=-1/3x+8

$y \geq \frac{3}{2} x - 3$ $y \leq - \frac{1}{3} x + 8$

Step 1

Graph $y \geq \frac{3}{2} x - 3$ .

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 $\frac{3}{2}$ and $x$ .

$y \geq \frac{3 x}{2} - 3$

Reorder terms.

$y \geq \frac{3}{2} x - 3$

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

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

$m = \frac{3}{2}$

$b = - 3$

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

Slope: $\frac{3}{2}$

y-intercept: $(0, - 3)$

Slope: $\frac{3}{2}$

y-intercept: $(0, - 3)$

Slope: $\frac{3}{2}$

y-intercept: $(0, - 3)$

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $\frac{3}{2} x - 3$ .

$y \geq \frac{3}{2} x - 3$

Step 2

Graph $y \leq - \frac{1}{3} x + 8$ .

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 $x$ and $\frac{1}{3}$ .

$y \leq - \frac{x}{3} + 8$

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

Reorder terms.

$y \leq - (\frac{1}{3} x) + 8$

Remove parentheses.

$y \leq - \frac{1}{3} x + 8$

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

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

$m = - \frac{1}{3}$

$b = 8$

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

Slope: $- \frac{1}{3}$

y-intercept: $(0, 8)$

Slope: $- \frac{1}{3}$

y-intercept: $(0, 8)$

Slope: $- \frac{1}{3}$

y-intercept: $(0, 8)$

Graph a solid line, then shade the area below the boundary line since $y$ is less than $- \frac{1}{3} x + 8$ .

$y \leq - \frac{1}{3} x + 8$

Step 3

Plot each graph on the same coordinate system.

$y \geq \frac{3}{2} x - 3$

$y \leq - \frac{1}{3} x + 8$

Step 4

Graph y>=3/2x-3 y<=-1/3x+8

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