Graph -7x+3y>-1 5x-9y>-6

$- 7 x + 3 y > - 1$ $5 x - 9 y > - 6$

Step 1

Graph $- 7 x + 3 y > - 1$ .

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

Solve for $y$ .

Add $7 x$ to both sides of the inequality.

$3 y > - 1 + 7 x$

Divide each term in $3 y > - 1 + 7 x$ by $3$ and simplify.

Divide each term in $3 y > - 1 + 7 x$ by $3$ .

$\frac{3 y}{3} > \frac{- 1}{3} + \frac{7 x}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} > \frac{- 1}{3} + \frac{7 x}{3}$

Divide $y$ by $1$ .

$y > \frac{- 1}{3} + \frac{7 x}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$y > - \frac{1}{3} + \frac{7 x}{3}$

Rearrange terms.

$y > \frac{7 x}{3} - \frac{1}{3}$

Reorder terms.

$y > \frac{7}{3} x - \frac{1}{3}$

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

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

$m = \frac{7}{3}$

$b = - \frac{1}{3}$

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

Slope: $\frac{7}{3}$

y-intercept: $(0, - \frac{1}{3})$

Slope: $\frac{7}{3}$

y-intercept: $(0, - \frac{1}{3})$

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $\frac{7}{3} x - \frac{1}{3}$ .

$y > \frac{7}{3} x - \frac{1}{3}$

Step 2

Graph $5 x - 9 y > - 6$ .

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

Solve for $y$ .

Subtract $5 x$ from both sides of the inequality.

$- 9 y > - 6 - 5 x$

Divide each term in $- 9 y > - 6 - 5 x$ by $- 9$ and simplify.

Divide each term in $- 9 y > - 6 - 5 x$ by $- 9$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 9 y}{- 9} < \frac{- 6}{- 9} + \frac{- 5 x}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 y}{- 9} < \frac{- 6}{- 9} + \frac{- 5 x}{- 9}$

Divide $y$ by $1$ .

$y < \frac{- 6}{- 9} + \frac{- 5 x}{- 9}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 6$ and $- 9$ .

Factor $- 3$ out of $- 6$ .

$y < \frac{- 3 (2)}{- 9} + \frac{- 5 x}{- 9}$

Cancel the common factors.

Factor $- 3$ out of $- 9$ .

$y < \frac{- 3 \cdot 2}{- 3 \cdot 3} + \frac{- 5 x}{- 9}$

Cancel the common factor.

$y < \frac{- 3 \cdot 2}{- 3 \cdot 3} + \frac{- 5 x}{- 9}$

Rewrite the expression.

$y < \frac{2}{3} + \frac{- 5 x}{- 9}$

Dividing two negative values results in a positive value.

$y < \frac{2}{3} + \frac{5 x}{9}$

Rearrange terms.

$y < \frac{5 x}{9} + \frac{2}{3}$

Reorder terms.

$y < \frac{5}{9} x + \frac{2}{3}$

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

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

$m = \frac{5}{9}$

$b = \frac{2}{3}$

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

Slope: $\frac{5}{9}$

y-intercept: $(0, \frac{2}{3})$

Slope: $\frac{5}{9}$

y-intercept: $(0, \frac{2}{3})$

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $\frac{5}{9} x + \frac{2}{3}$ .

$y < \frac{5}{9} x + \frac{2}{3}$

Step 3

Plot each graph on the same coordinate system.

$- 7 x + 3 y > - 1$

$5 x - 9 y > - 6$

Step 4

Graph -7x+3y>-1 5x-9y>-6

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