Graph x-6y>5 7x+2y>=4

$x - 6 y > 5$ $7 x + 2 y \geq 4$

Graph $x - 6 y > 5$ .

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

Solve for $y$ .

Subtract $x$ from both sides of the inequality.

$- 6 y > 5 - x$

Divide each term in $- 6 y > 5 - x$ by $- 6$ and simplify.

Divide each term in $- 6 y > 5 - x$ by $- 6$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 6 y}{- 6} < \frac{5}{- 6} + \frac{- x}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} < \frac{5}{- 6} + \frac{- x}{- 6}$

Divide $y$ by $1$ .

$y < \frac{5}{- 6} + \frac{- x}{- 6}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y < - \frac{5}{6} + \frac{- x}{- 6}$

Dividing two negative values results in a positive value.

$y < - \frac{5}{6} + \frac{x}{6}$

Rearrange terms.

$y < \frac{x}{6} - \frac{5}{6}$

Reorder terms.

$y < \frac{1}{6} x - \frac{5}{6}$

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

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

$m = \frac{1}{6}$

$b = - \frac{5}{6}$

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

Slope: $\frac{1}{6}$

y-intercept: $(0, - \frac{5}{6})$

Slope: $\frac{1}{6}$

y-intercept: $(0, - \frac{5}{6})$

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $\frac{1}{6} x - \frac{5}{6}$ .

$y < \frac{1}{6} x - \frac{5}{6}$

Graph $7 x + 2 y \geq 4$ .

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

Solve for $y$ .

Subtract $7 x$ from both sides of the inequality.

$2 y \geq 4 - 7 x$

Divide each term in $2 y \geq 4 - 7 x$ by $2$ and simplify.

Divide each term in $2 y \geq 4 - 7 x$ by $2$ .

$\frac{2 y}{2} \geq \frac{4}{2} + \frac{- 7 x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} \geq \frac{4}{2} + \frac{- 7 x}{2}$

Divide $y$ by $1$ .

$y \geq \frac{4}{2} + \frac{- 7 x}{2}$

Simplify the right side.

Simplify each term.

Divide $4$ by $2$ .

$y \geq 2 + \frac{- 7 x}{2}$

Move the negative in front of the fraction.

$y \geq 2 - \frac{7 x}{2}$

Rearrange terms.

$y \geq - \frac{7 x}{2} + 2$

Reorder terms.

$y \geq - (\frac{7}{2} x) + 2$

Remove parentheses.

$y \geq - \frac{7}{2} x + 2$

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

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

$m = - \frac{7}{2}$

$b = 2$

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

Slope: $- \frac{7}{2}$

y-intercept: $(0, 2)$

Slope: $- \frac{7}{2}$

y-intercept: $(0, 2)$

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $- \frac{7}{2} x + 2$ .

$y \geq - \frac{7}{2} x + 2$

Plot each graph on the same coordinate system.

$x - 6 y > 5$

$7 x + 2 y \geq 4$

Graph x-6y>5 7x+2y>=4

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