Graph 5x+6y<=30

$5 x + 6 y \leq 30$

Step 1

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

Solve for $y$ .

Subtract $5 x$ from both sides of the inequality.

$6 y \leq 30 - 5 x$

Divide each term in $6 y \leq 30 - 5 x$ by $6$ and simplify.

Divide each term in $6 y \leq 30 - 5 x$ by $6$ .

$\frac{6 y}{6} \leq \frac{30}{6} + \frac{- 5 x}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} \leq \frac{30}{6} + \frac{- 5 x}{6}$

Divide $y$ by $1$ .

$y \leq \frac{30}{6} + \frac{- 5 x}{6}$

Simplify the right side.

Simplify each term.

Divide $30$ by $6$ .

$y \leq 5 + \frac{- 5 x}{6}$

Move the negative in front of the fraction.

$y \leq 5 - \frac{5 x}{6}$

Rearrange terms.

$y \leq - \frac{5 x}{6} + 5$

Reorder terms.

$y \leq - (\frac{5}{6} x) + 5$

Remove parentheses.

$y \leq - \frac{5}{6} x + 5$

Step 2

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

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

$m = - \frac{5}{6}$

$b = 5$

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

Slope: $- \frac{5}{6}$

y-intercept: $(0, 5)$

Slope: $- \frac{5}{6}$

y-intercept: $(0, 5)$

Step 3

Graph a solid line, then shade the area below the boundary line since $y$ is less than $- \frac{5}{6} x + 5$ .

$y \leq - \frac{5}{6} x + 5$

Step 4