Graph x+2y>=6 x+2y>=-10

$x + 2 y \geq 6$ $x + 2 y \geq - 10$

Step 1

Graph $x + 2 y \geq 6$ .

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

Solve for $y$ .

Subtract $x$ from both sides of the inequality.

$2 y \geq 6 - x$

Divide each term in $2 y \geq 6 - x$ by $2$ and simplify.

Divide each term in $2 y \geq 6 - x$ by $2$ .

$\frac{2 y}{2} \geq \frac{6}{2} + \frac{- x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} \geq \frac{6}{2} + \frac{- x}{2}$

Divide $y$ by $1$ .

$y \geq \frac{6}{2} + \frac{- x}{2}$

Simplify the right side.

Simplify each term.

Divide $6$ by $2$ .

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

Move the negative in front of the fraction.

$y \geq 3 - \frac{x}{2}$

Rearrange terms.

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

Reorder terms.

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

Remove parentheses.

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

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: $(0, 3)$

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

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

Step 2

Graph $x + 2 y \geq - 10$ .

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

Solve for $y$ .

Subtract $x$ from both sides of the inequality.

$2 y \geq - 10 - x$

Divide each term in $2 y \geq - 10 - x$ by $2$ and simplify.

Divide each term in $2 y \geq - 10 - x$ by $2$ .

$\frac{2 y}{2} \geq \frac{- 10}{2} + \frac{- x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} \geq \frac{- 10}{2} + \frac{- x}{2}$

Divide $y$ by $1$ .

$y \geq \frac{- 10}{2} + \frac{- x}{2}$

Simplify the right side.

Simplify each term.

Divide $- 10$ by $2$ .

$y \geq - 5 + \frac{- x}{2}$

Move the negative in front of the fraction.

$y \geq - 5 - \frac{x}{2}$

Rearrange terms.

$y \geq - \frac{x}{2} - 5$

Reorder terms.

$y \geq - (\frac{1}{2} x) - 5$

Remove parentheses.

$y \geq - \frac{1}{2} x - 5$

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

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

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

$b = - 5$

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: $(0, - 5)$

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

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

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $- \frac{1}{2} x - 5$ .

$y \geq - \frac{1}{2} x - 5$

Step 3

Plot each graph on the same coordinate system.

$x + 2 y \geq 6$

$x + 2 y \geq - 10$

Step 4

Graph x+2y>=6 x+2y>=-10

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