Graph 7x-9y<5 -2x+4y>5

$7 x - 9 y < 5$ $- 2 x + 4 y > 5$

Step 1

Graph $7 x - 9 y < 5$ .

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

Solve for $y$ .

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

$- 9 y < 5 - 7 x$

Divide each term in $- 9 y < 5 - 7 x$ by $- 9$ and simplify.

Divide each term in $- 9 y < 5 - 7 x$ by $- 9$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 9 y}{- 9} > \frac{5}{- 9} + \frac{- 7 x}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 y}{- 9} > \frac{5}{- 9} + \frac{- 7 x}{- 9}$

Divide $y$ by $1$ .

$y > \frac{5}{- 9} + \frac{- 7 x}{- 9}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y > - \frac{5}{9} + \frac{- 7 x}{- 9}$

Dividing two negative values results in a positive value.

$y > - \frac{5}{9} + \frac{7 x}{9}$

Rearrange terms.

$y > \frac{7 x}{9} - \frac{5}{9}$

Reorder terms.

$y > \frac{7}{9} x - \frac{5}{9}$

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

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

$m = \frac{7}{9}$

$b = - \frac{5}{9}$

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

Slope: $\frac{7}{9}$

y-intercept: $(0, - \frac{5}{9})$

Slope: $\frac{7}{9}$

y-intercept: $(0, - \frac{5}{9})$

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $\frac{7}{9} x - \frac{5}{9}$ .

$y > \frac{7}{9} x - \frac{5}{9}$

Step 2

Graph $- 2 x + 4 y > 5$ .

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

Solve for $y$ .

Add $2 x$ to both sides of the inequality.

$4 y > 5 + 2 x$

Divide each term in $4 y > 5 + 2 x$ by $4$ and simplify.

Divide each term in $4 y > 5 + 2 x$ by $4$ .

$\frac{4 y}{4} > \frac{5}{4} + \frac{2 x}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} > \frac{5}{4} + \frac{2 x}{4}$

Divide $y$ by $1$ .

$y > \frac{5}{4} + \frac{2 x}{4}$

Simplify the right side.

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2 x$ .

$y > \frac{5}{4} + \frac{2 (x)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$y > \frac{5}{4} + \frac{2 x}{2 \cdot 2}$

Cancel the common factor.

$y > \frac{5}{4} + \frac{2 x}{2 \cdot 2}$

Rewrite the expression.

$y > \frac{5}{4} + \frac{x}{2}$

Rearrange terms.

$y > \frac{x}{2} + \frac{5}{4}$

Reorder terms.

$y > \frac{1}{2} x + \frac{5}{4}$

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

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

$m = \frac{1}{2}$

$b = \frac{5}{4}$

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

Slope: $\frac{1}{2}$

y-intercept: $(0, \frac{5}{4})$

Slope: $\frac{1}{2}$

y-intercept: $(0, \frac{5}{4})$

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $\frac{1}{2} x + \frac{5}{4}$ .

$y > \frac{1}{2} x + \frac{5}{4}$

Step 3

Plot each graph on the same coordinate system.

$7 x - 9 y < 5$

$- 2 x + 4 y > 5$

Step 4

Graph 7x-9y<5 -2x+4y>5

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