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

$y \geq - \frac{1}{2} x$ $y < \frac{1}{2} x + 1$

Step 1

Graph $y \geq - \frac{1}{2} x$ .

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 $\frac{1}{2}$ .

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

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

Reorder terms.

$y \geq - (\frac{1}{2} x)$

Remove parentheses.

$y \geq - \frac{1}{2} x$

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

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

$m = - \frac{1}{2}$

$b = 0$

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

Slope: $- \frac{1}{2}$

y-intercept: $(0, 0)$

Slope: $- \frac{1}{2}$

y-intercept: $(0, 0)$

Slope: $- \frac{1}{2}$

y-intercept: $(0, 0)$

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $- \frac{1}{2} x$ .

$y \geq - \frac{1}{2} x$

Step 2

Graph $y < \frac{1}{2} x + 1$ .

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 $\frac{1}{2}$ and $x$ .

$y < \frac{x}{2} + 1$

Reorder terms.

$y < \frac{1}{2} x + 1$

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

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

$m = \frac{1}{2}$

$b = 1$

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

Slope: $\frac{1}{2}$

y-intercept: $(0, 1)$

Slope: $\frac{1}{2}$

y-intercept: $(0, 1)$

Slope: $\frac{1}{2}$

y-intercept: $(0, 1)$

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $\frac{1}{2} x + 1$ .

$y < \frac{1}{2} x + 1$

Step 3

Plot each graph on the same coordinate system.

$y \geq - \frac{1}{2} x$

$y < \frac{1}{2} x + 1$

Step 4

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

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