Graph 3x-y<6 3x-y>-2

$3 x - y < 6$ $3 x - y > - 2$

Step 1

Graph $3 x - y < 6$ .

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

Solve for $y$ .

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

$- y < 6 - 3 x$

Divide each term in $- y < 6 - 3 x$ by $- 1$ and simplify.

Divide each term in $- y < 6 - 3 x$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} > \frac{6}{- 1} + \frac{- 3 x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} > \frac{6}{- 1} + \frac{- 3 x}{- 1}$

Divide $y$ by $1$ .

$y > \frac{6}{- 1} + \frac{- 3 x}{- 1}$

Simplify the right side.

Simplify each term.

Divide $6$ by $- 1$ .

$y > - 6 + \frac{- 3 x}{- 1}$

Move the negative one from the denominator of $\frac{- 3 x}{- 1}$ .

$y > - 6 - 1 \cdot (- 3 x)$

Rewrite $- 1 \cdot (- 3 x)$ as $- (- 3 x)$ .

$y > - 6 - (- 3 x)$

Multiply $- 3$ by $- 1$ .

$y > - 6 + 3 x$

Rearrange terms.

$y > 3 x - 6$

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 $y = m x + b$ .

$m = 3$

$b = - 6$

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

Slope: $3$

y-intercept: $(0, - 6)$

Slope: $3$

y-intercept: $(0, - 6)$

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $3 x - 6$ .

$y > 3 x - 6$

Step 2

Graph $3 x - y > - 2$ .

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

Solve for $y$ .

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

$- y > - 2 - 3 x$

Divide each term in $- y > - 2 - 3 x$ by $- 1$ and simplify.

Divide each term in $- y > - 2 - 3 x$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $- 2$ by $- 1$ .

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

Move the negative one from the denominator of $\frac{- 3 x}{- 1}$ .

$y < 2 - 1 \cdot (- 3 x)$

Rewrite $- 1 \cdot (- 3 x)$ as $- (- 3 x)$ .

$y < 2 - (- 3 x)$

Multiply $- 3$ by $- 1$ .

$y < 2 + 3 x$

Rearrange terms.

$y < 3 x + 2$

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 $y = m x + b$ .

$m = 3$

$b = 2$

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

Slope: $3$

y-intercept: $(0, 2)$

Slope: $3$

y-intercept: $(0, 2)$

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $3 x + 2$ .

$y < 3 x + 2$

Step 3

Plot each graph on the same coordinate system.

$3 x - y < 6$

$3 x - y > - 2$

Step 4

Graph 3x-y<6 3x-y>-2

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