Graph 2x+5y>=10

$2 x + 5 y \geq 10$

Step 1

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

Solve for $y$ .

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

$5 y \geq 10 - 2 x$

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

Divide each term in $5 y \geq 10 - 2 x$ by $5$ .

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

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 $5$ .

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

Move the negative in front of the fraction.

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

Rearrange terms.

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

Reorder terms.

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

Remove parentheses.

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

Step 2

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

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

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

$b = 2$

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: $(0, 2)$

Step 3

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

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

Step 4