Graph x+2y>=-7

$x + 2 y \geq - 7$

Step 1

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

Solve for $y$ .

Subtract $x$ from both sides of the inequality.

$2 y \geq - 7 - x$

Divide each term in $2 y \geq - 7 - x$ by $2$ and simplify.

Divide each term in $2 y \geq - 7 - x$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

Move the negative in front of the fraction.

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

Rearrange terms.

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

Reorder terms.

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

Remove parentheses.

$y \geq - \frac{1}{2} x - \frac{7}{2}$

Step 2

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

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

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

$b = - \frac{7}{2}$

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: $(0, - \frac{7}{2})$

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

y-intercept: $(0, - \frac{7}{2})$

Step 3

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $- \frac{1}{2} x - \frac{7}{2}$ .

$y \geq - \frac{1}{2} x - \frac{7}{2}$

Step 4