Graph 2x>=y+2 2x-5y<=10

$2 x \geq y + 2$ $2 x - 5 y \leq 10$

Graph $2 x \geq y + 2$ .

Solve for $y$ .

Rewrite so $y$ is on the left side of the inequality.

$y + 2 \leq 2 x$

Subtract $2$ from both sides of the inequality.

$y \leq 2 x - 2$

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 $2 x - 5 y \leq 10$ .

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

Solve for $y$ .

Subtract $2 x$ from both sides of the inequality.

$- 5 y \leq 10 - 2 x$

Divide each term in $- 5 y \leq 10 - 2 x$ by $- 5$ and simplify.

Divide each term in $- 5 y \leq 10 - 2 x$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 y}{- 5} \geq \frac{10}{- 5} + \frac{- 2 x}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 y}{- 5} \geq \frac{10}{- 5} + \frac{- 2 x}{- 5}$

Divide $y$ by $1$ .

$y \geq \frac{10}{- 5} + \frac{- 2 x}{- 5}$

Simplify the right side.

Simplify each term.

Divide $10$ by $- 5$ .

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

Dividing two negative values results in a positive value.

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

Rearrange terms.

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

Reorder terms.

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

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

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

$m = \frac{2}{5}$

$b = - 2$

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

Slope: $\frac{2}{5}$

y-intercept: $(0, - 2)$

Slope: $\frac{2}{5}$

y-intercept: $(0, - 2)$

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

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

Plot each graph on the same coordinate system.

$2 x \geq y + 2$

$2 x - 5 y \leq 10$

Graph 2x>=y+2 2x-5y<=10

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