Graph y>-1/6x+5 y<3/2x-5

$y > - \frac{1}{6} x + 5$ $y < \frac{3}{2} x - 5$

Graph $y > - \frac{1}{6} x + 5$ .

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 $x$ and $\frac{1}{6}$ .

$y > - \frac{x}{6} + 5$

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

Reorder terms.

$y > - (\frac{1}{6} x) + 5$

Remove parentheses.

$y > - \frac{1}{6} x + 5$

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

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

$m = - \frac{1}{6}$

$b = 5$

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

Slope: $- \frac{1}{6}$

y-intercept: $(0, 5)$

Slope: $- \frac{1}{6}$

y-intercept: $(0, 5)$

Slope: $- \frac{1}{6}$

y-intercept: $(0, 5)$

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $- \frac{1}{6} x + 5$ .

$y > - \frac{1}{6} x + 5$

Graph $y < \frac{3}{2} x - 5$ .

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

$y < \frac{3 x}{2} - 5$

Reorder terms.

$y < \frac{3}{2} x - 5$

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

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

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

$b = - 5$

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: $(0, - 5)$

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

y-intercept: $(0, - 5)$

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

y-intercept: $(0, - 5)$

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $\frac{3}{2} x - 5$ .

$y < \frac{3}{2} x - 5$

Plot each graph on the same coordinate system.

$y > - \frac{1}{6} x + 5$

$y < \frac{3}{2} x - 5$

Graph y>-1/6x+5 y<3/2x-5

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