Graph 3x+4y<20 x-2y<0

$3 x + 4 y < 20$ $x - 2 y < 0$

Step 1

Graph $3 x + 4 y < 20$ .

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

Solve for $y$ .

Subtract $3 x$ from both sides of the inequality.

$4 y < 20 - 3 x$

Divide each term in $4 y < 20 - 3 x$ by $4$ and simplify.

Divide each term in $4 y < 20 - 3 x$ by $4$ .

$\frac{4 y}{4} < \frac{20}{4} + \frac{- 3 x}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} < \frac{20}{4} + \frac{- 3 x}{4}$

Divide $y$ by $1$ .

$y < \frac{20}{4} + \frac{- 3 x}{4}$

Simplify the right side.

Simplify each term.

Divide $20$ by $4$ .

$y < 5 + \frac{- 3 x}{4}$

Move the negative in front of the fraction.

$y < 5 - \frac{3 x}{4}$

Rearrange terms.

$y < - \frac{3 x}{4} + 5$

Reorder terms.

$y < - (\frac{3}{4} x) + 5$

Remove parentheses.

$y < - \frac{3}{4} x + 5$

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

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

$m = - \frac{3}{4}$

$b = 5$

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

Slope: $- \frac{3}{4}$

y-intercept: $(0, 5)$

Slope: $- \frac{3}{4}$

y-intercept: $(0, 5)$

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $- \frac{3}{4} x + 5$ .

$y < - \frac{3}{4} x + 5$

Step 2

Graph $x - 2 y < 0$ .

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

Solve for $y$ .

Subtract $x$ from both sides of the inequality.

$- 2 y < - x$

Divide each term in $- 2 y < - x$ by $- 2$ and simplify.

Divide each term in $- 2 y < - x$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 y}{- 2} > \frac{- x}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} > \frac{- x}{- 2}$

Divide $y$ by $1$ .

$y > \frac{- x}{- 2}$

Simplify the right side.

Dividing two negative values results in a positive value.

$y > \frac{x}{2}$

Reorder terms.

$y > \frac{1}{2} x$

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

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

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

$b = 0$

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: $(0, 0)$

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

y-intercept: $(0, 0)$

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

$y > \frac{1}{2} x$

Step 3

Plot each graph on the same coordinate system.

$3 x + 4 y < 20$

$x - 2 y < 0$

Step 4

Graph 3x+4y<20 x-2y<0

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