Graph 5y-6x>30

$5 y - 6 x > 30$

Step 1

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

Solve for $y$ .

Add $6 x$ to both sides of the inequality.

$5 y > 30 + 6 x$

Divide each term in $5 y > 30 + 6 x$ by $5$ and simplify.

Divide each term in $5 y > 30 + 6 x$ by $5$ .

$\frac{5 y}{5} > \frac{30}{5} + \frac{6 x}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} > \frac{30}{5} + \frac{6 x}{5}$

Divide $y$ by $1$ .

$y > \frac{30}{5} + \frac{6 x}{5}$

Simplify the right side.

Divide $30$ by $5$ .

$y > 6 + \frac{6 x}{5}$

Rearrange terms.

$y > \frac{6 x}{5} + 6$

Reorder terms.

$y > \frac{6}{5} x + 6$

Step 2

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

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

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

$b = 6$

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

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

y-intercept: $(0, 6)$

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

y-intercept: $(0, 6)$

Step 3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $\frac{6}{5} x + 6$ .

$y > \frac{6}{5} x + 6$

Step 4