Graph 8x-2y>6 32x-8y>-24

$8 x - 2 y > 6$ $32 x - 8 y > - 24$

Graph $8 x - 2 y > 6$ .

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

Solve for $y$ .

Subtract $8 x$ from both sides of the inequality.

$- 2 y > 6 - 8 x$

Divide each term in $- 2 y > 6 - 8 x$ by $- 2$ and simplify.

Divide each term in $- 2 y > 6 - 8 x$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 y}{- 2} < \frac{6}{- 2} + \frac{- 8 x}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} < \frac{6}{- 2} + \frac{- 8 x}{- 2}$

Divide $y$ by $1$ .

$y < \frac{6}{- 2} + \frac{- 8 x}{- 2}$

Simplify the right side.

Simplify each term.

Divide $6$ by $- 2$ .

$y < - 3 + \frac{- 8 x}{- 2}$

Cancel the common factor of $- 8$ and $- 2$ .

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

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

Cancel the common factors.

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

$y < - 3 + \frac{- 2 (4 x)}{- 2 (1)}$

Cancel the common factor.

$y < - 3 + \frac{- 2 (4 x)}{- 2 \cdot 1}$

Rewrite the expression.

$y < - 3 + \frac{4 x}{1}$

Divide $4 x$ by $1$ .

$y < - 3 + 4 x$

Rearrange terms.

$y < 4 x - 3$

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 $y = m x + b$ .

$m = 4$

$b = - 3$

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

Slope: $4$

y-intercept: $(0, - 3)$

Slope: $4$

y-intercept: $(0, - 3)$

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $4 x - 3$ .

$y < 4 x - 3$

Graph $32 x - 8 y > - 24$ .

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

Solve for $y$ .

Subtract $32 x$ from both sides of the inequality.

$- 8 y > - 24 - 32 x$

Divide each term in $- 8 y > - 24 - 32 x$ by $- 8$ and simplify.

Divide each term in $- 8 y > - 24 - 32 x$ by $- 8$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 8 y}{- 8} < \frac{- 24}{- 8} + \frac{- 32 x}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} < \frac{- 24}{- 8} + \frac{- 32 x}{- 8}$

Divide $y$ by $1$ .

$y < \frac{- 24}{- 8} + \frac{- 32 x}{- 8}$

Simplify the right side.

Simplify each term.

Divide $- 24$ by $- 8$ .

$y < 3 + \frac{- 32 x}{- 8}$

Cancel the common factor of $- 32$ and $- 8$ .

Factor $- 8$ out of $- 32 x$ .

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

Cancel the common factors.

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

$y < 3 + \frac{- 8 (4 x)}{- 8 (1)}$

Cancel the common factor.

$y < 3 + \frac{- 8 (4 x)}{- 8 \cdot 1}$

Rewrite the expression.

$y < 3 + \frac{4 x}{1}$

Divide $4 x$ by $1$ .

$y < 3 + 4 x$

Rearrange terms.

$y < 4 x + 3$

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 $y = m x + b$ .

$m = 4$

$b = 3$

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

Slope: $4$

y-intercept: $(0, 3)$

Slope: $4$

y-intercept: $(0, 3)$

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $4 x + 3$ .

$y < 4 x + 3$

Plot each graph on the same coordinate system.

$8 x - 2 y > 6$

$32 x - 8 y > - 24$

Graph 8x-2y>6 32x-8y>-24

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