Graph 4x+4y<16 x>y+16

$4 x + 4 y < 16$ $x > y + 16$

Step 1

Graph $4 x + 4 y < 16$ .

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

Solve for $y$ .

Subtract $4 x$ from both sides of the inequality.

$4 y < 16 - 4 x$

Divide each term in $4 y < 16 - 4 x$ by $4$ and simplify.

Divide each term in $4 y < 16 - 4 x$ by $4$ .

$\frac{4 y}{4} < \frac{16}{4} + \frac{- 4 x}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} < \frac{16}{4} + \frac{- 4 x}{4}$

Divide $y$ by $1$ .

$y < \frac{16}{4} + \frac{- 4 x}{4}$

Simplify the right side.

Simplify each term.

Divide $16$ by $4$ .

$y < 4 + \frac{- 4 x}{4}$

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

Factor $4$ out of $- 4 x$ .

$y < 4 + \frac{4 (- x)}{4}$

Cancel the common factors.

Factor $4$ out of $4$ .

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

Cancel the common factor.

$y < 4 + \frac{4 (- x)}{4 \cdot 1}$

Rewrite the expression.

$y < 4 + \frac{- x}{1}$

Divide $- x$ by $1$ .

$y < 4 - x$

Rearrange terms.

$y < - x + 4$

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 $y = m x + b$ .

$m = - 1$

$b = 4$

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

Slope: $- 1$

y-intercept: $(0, 4)$

Slope: $- 1$

y-intercept: $(0, 4)$

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $- x + 4$ .

$y < - x + 4$

Step 2

Graph $x > y + 16$ .

Solve for $y$ .

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

$y + 16 < x$

Subtract $16$ from both sides of the inequality.

$y < x - 16$

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 $y = m x + b$ .

$m = 1$

$b = - 16$

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

Slope: $1$

y-intercept: $(0, - 16)$

Slope: $1$

y-intercept: $(0, - 16)$

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $x - 16$ .

$y < x - 16$

Step 3

Plot each graph on the same coordinate system.

$4 x + 4 y < 16$

$x > y + 16$

Step 4

Graph 4x+4y<16 x>y+16

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