Graph 2(x-y)>=5

$2 (x - y) \geq 5$

Step 1

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

Solve for $y$ .

Divide each term in $2 (x - y) \geq 5$ by $2$ and simplify.

Divide each term in $2 (x - y) \geq 5$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x - y$ by $1$ .

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

Subtract $x$ from both sides of the inequality.

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

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

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

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative one from the denominator of $\frac{\frac{5}{2}}{- 1}$ .

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

Rewrite $- 1 \cdot \frac{5}{2}$ as $- \frac{5}{2}$ .

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

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

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

Rearrange terms.

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

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 $y = m x + b$ .

$m = 1$

$b = - \frac{5}{2}$

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

Slope: $1$

y-intercept: $(0, - \frac{5}{2})$

Slope: $1$

y-intercept: $(0, - \frac{5}{2})$

Step 3

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

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

Step 4

Graph 2(x-y)>=5

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