Graph y<=2x+2 1/2x+y<7 y-3>=0

$y \leq 2 x + 2$ $\frac{1}{2} x + y < 7$ $y - 3 \geq 0$

Graph $y \leq 2 x + 2$ .

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 $y = m x + b$ .

$m = 2$

$b = 2$

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

Slope: $2$

y-intercept: $(0, 2)$

Slope: $2$

y-intercept: $(0, 2)$

Graph a solid line, then shade the area below the boundary line since $y$ is less than $2 x + 2$ .

$y \leq 2 x + 2$

Graph $\frac{1}{2} x + y < 7$ .

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

Solve for $y$ .

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

$\frac{x}{2} + y < 7$

Subtract $\frac{x}{2}$ from both sides of the inequality.

$y < 7 - \frac{x}{2}$

Rearrange terms.

$y < - \frac{x}{2} + 7$

Reorder terms.

$y < - (\frac{1}{2} x) + 7$

Remove parentheses.

$y < - \frac{1}{2} x + 7$

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

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

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

$b = 7$

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: $(0, 7)$

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

y-intercept: $(0, 7)$

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $- \frac{1}{2} x + 7$ .

$y < - \frac{1}{2} x + 7$

Add $3$ to both sides of the inequality.

$y \geq 3$

Plot each graph on the same coordinate system.

$y \leq 2 x + 2$

$\frac{1}{2} x + y < 7$

$y - 3 \geq 0$