Graph -x+4y<=-16 -3x+y<2

$- x + 4 y \leq - 16$ $- 3 x + y < 2$

Step 1

Graph $- x + 4 y \leq - 16$ .

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

Solve for $y$ .

Add $x$ to both sides of the inequality.

$4 y \leq - 16 + x$

Divide each term in $4 y \leq - 16 + x$ by $4$ and simplify.

Divide each term in $4 y \leq - 16 + x$ by $4$ .

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Divide $- 16$ by $4$ .

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

Rearrange terms.

$y \leq \frac{x}{4} - 4$

Reorder terms.

$y \leq \frac{1}{4} x - 4$

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

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

$m = \frac{1}{4}$

$b = - 4$

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

Slope: $\frac{1}{4}$

y-intercept: $(0, - 4)$

Slope: $\frac{1}{4}$

y-intercept: $(0, - 4)$

Graph a solid line, then shade the area below the boundary line since $y$ is less than $\frac{1}{4} x - 4$ .

$y \leq \frac{1}{4} x - 4$

Step 2

Graph $- 3 x + y < 2$ .

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

Add $3 x$ to both sides of the inequality.

$y < 2 + 3 x$

Rearrange terms.

$y < 3 x + 2$

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 $y = m x + b$ .

$m = 3$

$b = 2$

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

Slope: $3$

y-intercept: $(0, 2)$

Slope: $3$

y-intercept: $(0, 2)$

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $3 x + 2$ .

$y < 3 x + 2$

Step 3

Plot each graph on the same coordinate system.

$- x + 4 y \leq - 16$

$- 3 x + y < 2$

Step 4

Graph -x+4y<=-16 -3x+y<2

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