Graph 2x+y<2 x-4y>9

$2 x + y < 2$ $x - 4 y > 9$

Graph $2 x + y < 2$ .

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

Subtract $2 x$ from both sides of the inequality.

$y < 2 - 2 x$

Rearrange terms.

$y < - 2 x + 2$

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 $y = m x + b$ .

$m = - 2$

$b = 2$

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

Slope: $- 2$

y-intercept: $(0, 2)$

Slope: $- 2$

y-intercept: $(0, 2)$

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

$y < - 2 x + 2$

Graph $x - 4 y > 9$ .

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

Solve for $y$ .

Subtract $x$ from both sides of the inequality.

$- 4 y > 9 - x$

Divide each term in $- 4 y > 9 - x$ by $- 4$ and simplify.

Divide each term in $- 4 y > 9 - x$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 y}{- 4} < \frac{9}{- 4} + \frac{- x}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} < \frac{9}{- 4} + \frac{- x}{- 4}$

Divide $y$ by $1$ .

$y < \frac{9}{- 4} + \frac{- x}{- 4}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y < - \frac{9}{4} + \frac{- x}{- 4}$

Dividing two negative values results in a positive value.

$y < - \frac{9}{4} + \frac{x}{4}$

Rearrange terms.

$y < \frac{x}{4} - \frac{9}{4}$

Reorder terms.

$y < \frac{1}{4} x - \frac{9}{4}$

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

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

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

$b = - \frac{9}{4}$

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: $(0, - \frac{9}{4})$

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

y-intercept: $(0, - \frac{9}{4})$

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $\frac{1}{4} x - \frac{9}{4}$ .

$y < \frac{1}{4} x - \frac{9}{4}$

Plot each graph on the same coordinate system.

$2 x + y < 2$

$x - 4 y > 9$

Graph 2x+y<2 x-4y>9

Related Questions

Support LCMGCF.com by disabling your adblocker.