Graph y-2x<=-3 y-4<=-2x y>-1/4x

$y - 2 x \leq - 3$ $y - 4 \leq - 2 x$ $y > - \frac{1}{4} x$

Step 1

Graph $y - 2 x \leq - 3$ .

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

Add $2 x$ to both sides of the inequality.

$y \leq - 3 + 2 x$

Rearrange terms.

$y \leq 2 x - 3$

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 $y = m x + b$ .

$m = 2$

$b = - 3$

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

Slope: $2$

y-intercept: $(0, - 3)$

Slope: $2$

y-intercept: $(0, - 3)$

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

$y \leq 2 x - 3$

Step 2

Graph $y - 4 \leq - 2 x$ .

Add $4$ to both sides of the inequality.

$y \leq - 2 x + 4$

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 $y = m x + b$ .

$m = - 2$

$b = 4$

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

Slope: $- 2$

y-intercept: $(0, 4)$

Slope: $- 2$

y-intercept: $(0, 4)$

Graph a solid line, then shade the area below the boundary line since $y$ is less than $- 2 x + 4$ .

$y \leq - 2 x + 4$

Step 3

Graph $y > - \frac{1}{4} x$ .

Find the slope and the y-intercept for the boundary line.

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Simplify the right side.

Combine $x$ and $\frac{1}{4}$ .

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

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

Reorder terms.

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

Remove parentheses.

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

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

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

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

$b = 0$

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: $(0, 0)$

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

y-intercept: $(0, 0)$

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

y-intercept: $(0, 0)$

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

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

Step 4

Plot each graph on the same coordinate system.

$y - 2 x \leq - 3$

$y - 4 \leq - 2 x$

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

Step 5

Graph y-2x<=-3 y-4<=-2x y>-1/4x

Related Questions

Support LCMGCF.com by disabling your adblocker.