Graph x-y>7 8x+3y>=12

$x - y > 7$ $8 x + 3 y \geq 12$

Step 1

Graph $x - y > 7$ .

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

Solve for $y$ .

Subtract $x$ from both sides of the inequality.

$- y > 7 - x$

Divide each term in $- y > 7 - x$ by $- 1$ and simplify.

Divide each term in $- y > 7 - x$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} < \frac{7}{- 1} + \frac{- x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} < \frac{7}{- 1} + \frac{- x}{- 1}$

Divide $y$ by $1$ .

$y < \frac{7}{- 1} + \frac{- x}{- 1}$

Simplify the right side.

Simplify each term.

Divide $7$ by $- 1$ .

$y < - 7 + \frac{- x}{- 1}$

Dividing two negative values results in a positive value.

$y < - 7 + \frac{x}{1}$

Divide $x$ by $1$ .

$y < - 7 + x$

Rearrange terms.

$y < x - 7$

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 $y = m x + b$ .

$m = 1$

$b = - 7$

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

Slope: $1$

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

Slope: $1$

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

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $x - 7$ .

$y < x - 7$

Step 2

Graph $8 x + 3 y \geq 12$ .

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

Solve for $y$ .

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

$3 y \geq 12 - 8 x$

Divide each term in $3 y \geq 12 - 8 x$ by $3$ and simplify.

Divide each term in $3 y \geq 12 - 8 x$ by $3$ .

$\frac{3 y}{3} \geq \frac{12}{3} + \frac{- 8 x}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} \geq \frac{12}{3} + \frac{- 8 x}{3}$

Divide $y$ by $1$ .

$y \geq \frac{12}{3} + \frac{- 8 x}{3}$

Simplify the right side.

Simplify each term.

Divide $12$ by $3$ .

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

Move the negative in front of the fraction.

$y \geq 4 - \frac{8 x}{3}$

Rearrange terms.

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

Reorder terms.

$y \geq - (\frac{8}{3} x) + 4$

Remove parentheses.

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

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

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

$m = - \frac{8}{3}$

$b = 4$

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

Slope: $- \frac{8}{3}$

y-intercept: $(0, 4)$

Slope: $- \frac{8}{3}$

y-intercept: $(0, 4)$

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $- \frac{8}{3} x + 4$ .

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

Step 3

Plot each graph on the same coordinate system.

$x - y > 7$

$8 x + 3 y \geq 12$

Step 4

Graph x-y>7 8x+3y>=12

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