Graph 8x+4y>=10 3x-6y>12

$8 x + 4 y \geq 10$ $3 x - 6 y > 12$

Step 1

Graph $8 x + 4 y \geq 10$ .

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

Solve for $y$ .

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

$4 y \geq 10 - 8 x$

Divide each term in $4 y \geq 10 - 8 x$ by $4$ and simplify.

Divide each term in $4 y \geq 10 - 8 x$ by $4$ .

$\frac{4 y}{4} \geq \frac{10}{4} + \frac{- 8 x}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} \geq \frac{10}{4} + \frac{- 8 x}{4}$

Divide $y$ by $1$ .

$y \geq \frac{10}{4} + \frac{- 8 x}{4}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $10$ and $4$ .

Factor $2$ out of $10$ .

$y \geq \frac{2 (5)}{4} + \frac{- 8 x}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$y \geq \frac{2 \cdot 5}{2 \cdot 2} + \frac{- 8 x}{4}$

Cancel the common factor.

$y \geq \frac{2 \cdot 5}{2 \cdot 2} + \frac{- 8 x}{4}$

Rewrite the expression.

$y \geq \frac{5}{2} + \frac{- 8 x}{4}$

Cancel the common factor of $- 8$ and $4$ .

Factor $4$ out of $- 8 x$ .

$y \geq \frac{5}{2} + \frac{4 (- 2 x)}{4}$

Cancel the common factors.

Factor $4$ out of $4$ .

$y \geq \frac{5}{2} + \frac{4 (- 2 x)}{4 (1)}$

Cancel the common factor.

$y \geq \frac{5}{2} + \frac{4 (- 2 x)}{4 \cdot 1}$

Rewrite the expression.

$y \geq \frac{5}{2} + \frac{- 2 x}{1}$

Divide $- 2 x$ by $1$ .

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

Rearrange terms.

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

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 $y = m x + b$ .

$m = - 2$

$b = \frac{5}{2}$

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

Slope: $- 2$

y-intercept: $(0, \frac{5}{2})$

Slope: $- 2$

y-intercept: $(0, \frac{5}{2})$

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

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

Step 2

Graph $3 x - 6 y > 12$ .

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

Solve for $y$ .

Subtract $3 x$ from both sides of the inequality.

$- 6 y > 12 - 3 x$

Divide each term in $- 6 y > 12 - 3 x$ by $- 6$ and simplify.

Divide each term in $- 6 y > 12 - 3 x$ by $- 6$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 6 y}{- 6} < \frac{12}{- 6} + \frac{- 3 x}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} < \frac{12}{- 6} + \frac{- 3 x}{- 6}$

Divide $y$ by $1$ .

$y < \frac{12}{- 6} + \frac{- 3 x}{- 6}$

Simplify the right side.

Simplify each term.

Divide $12$ by $- 6$ .

$y < - 2 + \frac{- 3 x}{- 6}$

Cancel the common factor of $- 3$ and $- 6$ .

Factor $- 3$ out of $- 3 x$ .

$y < - 2 + \frac{- 3 (x)}{- 6}$

Cancel the common factors.

Factor $- 3$ out of $- 6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Rearrange terms.

$y < \frac{x}{2} - 2$

Reorder terms.

$y < \frac{1}{2} x - 2$

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

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

$m = \frac{1}{2}$

$b = - 2$

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

Slope: $\frac{1}{2}$

y-intercept: $(0, - 2)$

Slope: $\frac{1}{2}$

y-intercept: $(0, - 2)$

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $\frac{1}{2} x - 2$ .

$y < \frac{1}{2} x - 2$

Step 3

Plot each graph on the same coordinate system.

$8 x + 4 y \geq 10$

$3 x - 6 y > 12$

Step 4

Graph 8x+4y>=10 3x-6y>12

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