Graph 5x-6y<2y-x+8

$5 x - 6 y < 2 y - x + 8$

Step 1

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

Solve for $y$ .

Move all terms containing $y$ to the left side of the inequality.

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

$5 x - 6 y - 2 y < - x + 8$

Subtract $2 y$ from $- 6 y$ .

$5 x - 8 y < - x + 8$

Move all terms not containing $y$ to the right side of the inequality.

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

$- 8 y < - x + 8 - 5 x$

Subtract $5 x$ from $- x$ .

$- 8 y < - 6 x + 8$

Divide each term in $- 8 y < - 6 x + 8$ by $- 8$ and simplify.

Divide each term in $- 8 y < - 6 x + 8$ by $- 8$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 8 y}{- 8} > \frac{- 6 x}{- 8} + \frac{8}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} > \frac{- 6 x}{- 8} + \frac{8}{- 8}$

Divide $y$ by $1$ .

$y > \frac{- 6 x}{- 8} + \frac{8}{- 8}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 6$ and $- 8$ .

Factor $- 2$ out of $- 6 x$ .

$y > \frac{- 2 (3 x)}{- 8} + \frac{8}{- 8}$

Cancel the common factors.

Factor $- 2$ out of $- 8$ .

$y > \frac{- 2 (3 x)}{- 2 (4)} + \frac{8}{- 8}$

Cancel the common factor.

$y > \frac{- 2 (3 x)}{- 2 \cdot 4} + \frac{8}{- 8}$

Rewrite the expression.

$y > \frac{3 x}{4} + \frac{8}{- 8}$

Divide $8$ by $- 8$ .

$y > \frac{3 x}{4} - 1$

Reorder terms.

$y > \frac{3}{4} x - 1$

Step 2

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

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

$m = \frac{3}{4}$

$b = - 1$

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

Slope: $\frac{3}{4}$

y-intercept: $(0, - 1)$

Slope: $\frac{3}{4}$

y-intercept: $(0, - 1)$

Step 3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $\frac{3}{4} x - 1$ .

$y > \frac{3}{4} x - 1$

Step 4

Graph 5x-6y<2y-x+8

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