Graph x>-3y+4

$x > - 3 y + 4$

Step 1

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

Solve for $y$ .

Rewrite so $y$ is on the left side of the inequality.

$- 3 y + 4 < x$

Subtract $4$ from both sides of the inequality.

$- 3 y < x - 4$

Divide each term in $- 3 y < x - 4$ by $- 3$ and simplify.

Divide each term in $- 3 y < x - 4$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 y}{- 3} > \frac{x}{- 3} + \frac{- 4}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} > \frac{x}{- 3} + \frac{- 4}{- 3}$

Divide $y$ by $1$ .

$y > \frac{x}{- 3} + \frac{- 4}{- 3}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y > - \frac{x}{3} + \frac{- 4}{- 3}$

Dividing two negative values results in a positive value.

$y > - \frac{x}{3} + \frac{4}{3}$

Reorder terms.

$y > - (\frac{1}{3} x) + \frac{4}{3}$

Remove parentheses.

$y > - \frac{1}{3} x + \frac{4}{3}$

Step 2

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

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

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

$b = \frac{4}{3}$

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

Slope: $- \frac{1}{3}$

y-intercept: $(0, \frac{4}{3})$

Slope: $- \frac{1}{3}$

y-intercept: $(0, \frac{4}{3})$

Step 3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $- \frac{1}{3} x + \frac{4}{3}$ .

$y > - \frac{1}{3} x + \frac{4}{3}$

Step 4

Graph x>-3y+4

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