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

$6 x + 4 y > 12$ $3 x - 4 y > 8$

Step 1

Graph $6 x + 4 y > 12$ .

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

Solve for $y$ .

Subtract $6 x$ from both sides of the inequality.

$4 y > 12 - 6 x$

Divide each term in $4 y > 12 - 6 x$ by $4$ and simplify.

Divide each term in $4 y > 12 - 6 x$ by $4$ .

$\frac{4 y}{4} > \frac{12}{4} + \frac{- 6 x}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} > \frac{12}{4} + \frac{- 6 x}{4}$

Divide $y$ by $1$ .

$y > \frac{12}{4} + \frac{- 6 x}{4}$

Simplify the right side.

Simplify each term.

Divide $12$ by $4$ .

$y > 3 + \frac{- 6 x}{4}$

Cancel the common factor of $- 6$ and $4$ .

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

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

$y > 3 - \frac{3 x}{2}$

Rearrange terms.

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

Reorder terms.

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

Remove parentheses.

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

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

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

$m = - \frac{3}{2}$

$b = 3$

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

Slope: $- \frac{3}{2}$

y-intercept: $(0, 3)$

Slope: $- \frac{3}{2}$

y-intercept: $(0, 3)$

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $- \frac{3}{2} x + 3$ .

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

Step 2

Graph $3 x - 4 y > 8$ .

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

Solve for $y$ .

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

$- 4 y > 8 - 3 x$

Divide each term in $- 4 y > 8 - 3 x$ by $- 4$ and simplify.

Divide each term in $- 4 y > 8 - 3 x$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $8$ by $- 4$ .

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

Dividing two negative values results in a positive value.

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

Rearrange terms.

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

Reorder terms.

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

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

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

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

$b = - 2$

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: $(0, - 2)$

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

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

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $\frac{3}{4} x - 2$ .

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

Step 3

Plot each graph on the same coordinate system.

$6 x + 4 y > 12$

$3 x - 4 y > 8$

Step 4

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

Related Questions

Support LCMGCF.com by disabling your adblocker.