Graph y>=1/4x+5 y<1/4x+2

$y \geq \frac{1}{4} x + 5$ $y < \frac{1}{4} x + 2$

Step 1

Graph $y \geq \frac{1}{4} x + 5$ .

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

$y \geq \frac{x}{4} + 5$

Reorder terms.

$y \geq \frac{1}{4} x + 5$

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

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

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

$b = 5$

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: $(0, 5)$

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

y-intercept: $(0, 5)$

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

y-intercept: $(0, 5)$

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $\frac{1}{4} x + 5$ .

$y \geq \frac{1}{4} x + 5$

Step 2

Graph $y < \frac{1}{4} x + 2$ .

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

$y < \frac{x}{4} + 2$

Reorder terms.

$y < \frac{1}{4} x + 2$

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

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

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

$b = 2$

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: $(0, 2)$

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

y-intercept: $(0, 2)$

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

y-intercept: $(0, 2)$

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $\frac{1}{4} x + 2$ .

$y < \frac{1}{4} x + 2$

Step 3

Plot each graph on the same coordinate system.

$y \geq \frac{1}{4} x + 5$

$y < \frac{1}{4} x + 2$

Step 4

Graph y>=1/4x+5 y<1/4x+2

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