Graph y<-1/2x+3 y>1/2x+1 y<3x+10

$y < - \frac{1}{2} x + 3$ $y > \frac{1}{2} x + 1$ $y < 3 x + 10$

Step 1

Graph $y < - \frac{1}{2} x + 3$ .

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

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

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

Reorder terms.

$y < - (\frac{1}{2} x) + 3$

Remove parentheses.

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

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

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

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

$b = 3$

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: $(0, 3)$

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

y-intercept: $(0, 3)$

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

y-intercept: $(0, 3)$

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $- \frac{1}{2} x + 3$ .

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

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 above the boundary line since $y$ is greater than $\frac{1}{2} x + 1$ .

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

Step 3

Graph $y < 3 x + 10$ .

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 $y = m x + b$ .

$m = 3$

$b = 10$

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

Slope: $3$

y-intercept: $(0, 10)$

Slope: $3$

y-intercept: $(0, 10)$

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $3 x + 10$ .

$y < 3 x + 10$

Step 4

Plot each graph on the same coordinate system.

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

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

$y < 3 x + 10$

Step 5

Graph y<-1/2x+3 y>1/2x+1 y<3x+10

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