Graph 12x-5y<-30 12x-5y>35

$12 x - 5 y < - 30$ $12 x - 5 y > 35$

Step 1

Graph $12 x - 5 y < - 30$ .

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

Solve for $y$ .

Subtract $12 x$ from both sides of the inequality.

$- 5 y < - 30 - 12 x$

Divide each term in $- 5 y < - 30 - 12 x$ by $- 5$ and simplify.

Divide each term in $- 5 y < - 30 - 12 x$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 y}{- 5} > \frac{- 30}{- 5} + \frac{- 12 x}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 y}{- 5} > \frac{- 30}{- 5} + \frac{- 12 x}{- 5}$

Divide $y$ by $1$ .

$y > \frac{- 30}{- 5} + \frac{- 12 x}{- 5}$

Simplify the right side.

Simplify each term.

Divide $- 30$ by $- 5$ .

$y > 6 + \frac{- 12 x}{- 5}$

Dividing two negative values results in a positive value.

$y > 6 + \frac{12 x}{5}$

Rearrange terms.

$y > \frac{12 x}{5} + 6$

Reorder terms.

$y > \frac{12}{5} x + 6$

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

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

$m = \frac{12}{5}$

$b = 6$

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

Slope: $\frac{12}{5}$

y-intercept: $(0, 6)$

Slope: $\frac{12}{5}$

y-intercept: $(0, 6)$

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $\frac{12}{5} x + 6$ .

$y > \frac{12}{5} x + 6$

Step 2

Graph $12 x - 5 y > 35$ .

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

Solve for $y$ .

Subtract $12 x$ from both sides of the inequality.

$- 5 y > 35 - 12 x$

Divide each term in $- 5 y > 35 - 12 x$ by $- 5$ and simplify.

Divide each term in $- 5 y > 35 - 12 x$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 y}{- 5} < \frac{35}{- 5} + \frac{- 12 x}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 y}{- 5} < \frac{35}{- 5} + \frac{- 12 x}{- 5}$

Divide $y$ by $1$ .

$y < \frac{35}{- 5} + \frac{- 12 x}{- 5}$

Simplify the right side.

Simplify each term.

Divide $35$ by $- 5$ .

$y < - 7 + \frac{- 12 x}{- 5}$

Dividing two negative values results in a positive value.

$y < - 7 + \frac{12 x}{5}$

Rearrange terms.

$y < \frac{12 x}{5} - 7$

Reorder terms.

$y < \frac{12}{5} x - 7$

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

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

$m = \frac{12}{5}$

$b = - 7$

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

Slope: $\frac{12}{5}$

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

Slope: $\frac{12}{5}$

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

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $\frac{12}{5} x - 7$ .

$y < \frac{12}{5} x - 7$

Step 3

Plot each graph on the same coordinate system.

$12 x - 5 y < - 30$

$12 x - 5 y > 35$

Step 4

Graph 12x-5y<-30 12x-5y>35

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