Algebra Examples

$\frac{1}{3} x + 2 < y$ $x \geq - 3$

Step 1

Graph $\frac{1}{3} x + 2 < y$ .

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Step 1.1

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

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Step 1.1.1

Solve for $y$ .

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Step 1.1.1.1

Rewrite so $y$ is on the left side of the inequality.

$y > \frac{1}{3} x + 2$

Step 1.1.1.2

Combine $\frac{1}{3}$ and $x$ .

$y > \frac{x}{3} + 2$

Step 1.1.2

Reorder terms.

$y > \frac{1}{3} x + 2$

Step 1.2

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

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Step 1.2.1

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

$m = \frac{1}{3}$

$b = 2$

Step 1.2.2

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

Slope: $\frac{1}{3}$

y-intercept: $(0, 2)$

Slope: $\frac{1}{3}$

y-intercept: $(0, 2)$

Step 1.3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $\frac{1}{3} x + 2$ .

$y > \frac{1}{3} x + 2$

Step 2

Graph $x \geq - 3$ .

$x \geq - 3$

Step 3

Plot each graph on the same coordinate system.

$\frac{1}{3} x + 2 < y$

$x \geq - 3$

Step 4