Graph x-3y>=12 4x-3y>21

$x - 3 y \geq 12$ $4 x - 3 y > 21$

Graph $x - 3 y \geq 12$ .

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

Solve for $y$ .

Subtract $x$ from both sides of the inequality.

$- 3 y \geq 12 - x$

Divide each term in $- 3 y \geq 12 - x$ by $- 3$ and simplify.

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

$\frac{- 3 y}{- 3} \leq \frac{12}{- 3} + \frac{- x}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} \leq \frac{12}{- 3} + \frac{- x}{- 3}$

Divide $y$ by $1$ .

$y \leq \frac{12}{- 3} + \frac{- x}{- 3}$

Simplify the right side.

Simplify each term.

Divide $12$ by $- 3$ .

$y \leq - 4 + \frac{- x}{- 3}$

Dividing two negative values results in a positive value.

$y \leq - 4 + \frac{x}{3}$

Rearrange terms.

$y \leq \frac{x}{3} - 4$

Reorder terms.

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

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

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

$m = \frac{1}{3}$

$b = - 4$

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

Slope: $\frac{1}{3}$

y-intercept: $(0, - 4)$

Slope: $\frac{1}{3}$

y-intercept: $(0, - 4)$

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

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

Graph $4 x - 3 y > 21$ .

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

Solve for $y$ .

Subtract $4 x$ from both sides of the inequality.

$- 3 y > 21 - 4 x$

Divide each term in $- 3 y > 21 - 4 x$ by $- 3$ and simplify.

Divide each term in $- 3 y > 21 - 4 x$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 y}{- 3} < \frac{21}{- 3} + \frac{- 4 x}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} < \frac{21}{- 3} + \frac{- 4 x}{- 3}$

Divide $y$ by $1$ .

$y < \frac{21}{- 3} + \frac{- 4 x}{- 3}$

Simplify the right side.

Simplify each term.

Divide $21$ by $- 3$ .

$y < - 7 + \frac{- 4 x}{- 3}$

Dividing two negative values results in a positive value.

$y < - 7 + \frac{4 x}{3}$

Rearrange terms.

$y < \frac{4 x}{3} - 7$

Reorder terms.

$y < \frac{4}{3} x - 7$

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

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

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

$b = - 7$

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

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

y-intercept: $(0, - 7)$

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

y-intercept: $(0, - 7)$

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $\frac{4}{3} x - 7$ .

$y < \frac{4}{3} x - 7$

Plot each graph on the same coordinate system.

$x - 3 y \geq 12$

$4 x - 3 y > 21$

Graph x-3y>=12 4x-3y>21

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