Graph 2x-2/5y<=2

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

Step 1

Solve for $y$ .

Simplify each term.

Combine $y$ and $\frac{2}{5}$ .

$2 x - \frac{y \cdot 2}{5} \leq 2$

Move $2$ to the left of $y$ .

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

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

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

Divide each term in $- \frac{2 y}{5} \leq 2 - 2 x$ by $- 1$ and simplify.

Divide each term in $- \frac{2 y}{5} \leq 2 - 2 x$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $\frac{2 y}{5}$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $2$ by $- 1$ .

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

Move the negative one from the denominator of $\frac{- 2 x}{- 1}$ .

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

Rewrite $- 1 \cdot (- 2 x)$ as $- (- 2 x)$ .

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

Multiply $- 2$ by $- 1$ .

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

Multiply both sides by $5$ .

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

Simplify.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

$2 y \geq (- 2 + 2 x) \cdot 5$

Simplify the right side.

Simplify $(- 2 + 2 x) \cdot 5$ .

Apply the distributive property.

$2 y \geq - 2 \cdot 5 + 2 x \cdot 5$

Simplify the expression.

Multiply $- 2$ by $5$ .

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

Multiply $5$ by $2$ .

$2 y \geq - 10 + 10 x$

Reorder $- 10$ and $10 x$ .

$2 y \geq 10 x - 10$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Cancel the common factor of $10$ and $2$ .

Factor $2$ out of $10 x$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

$y \geq \frac{2 (5 x)}{2 (1)} + \frac{- 10}{2}$

Cancel the common factor.

$y \geq \frac{2 (5 x)}{2 \cdot 1} + \frac{- 10}{2}$

Rewrite the expression.

$y \geq \frac{5 x}{1} + \frac{- 10}{2}$

Divide $5 x$ by $1$ .

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

Divide $- 10$ by $2$ .

$y \geq 5 x - 5$

Step 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 $y = m x + b$ .

$m = 5$

$b = - 5$

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

Slope: $5$

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

Slope: $5$

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

Step 3

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

$y \geq 5 x - 5$

Step 4

Graph 2x-2/5y<=2

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