Algebra Examples

$\frac{5}{2} x - y < 3$

Step 1

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

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Step 1.1

Solve for $y$ .

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Step 1.1.1

Combine $\frac{5}{2}$ and $x$ .

$\frac{5 x}{2} - y < 3$

Step 1.1.2

Subtract $\frac{5 x}{2}$ from both sides of the inequality.

$- y < 3 - \frac{5 x}{2}$

Step 1.1.3

Divide each term in $- y < 3 - \frac{5 x}{2}$ by $- 1$ and simplify.

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Step 1.1.3.1

Divide each term in $- y < 3 - \frac{5 x}{2}$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} > \frac{3}{- 1} + \frac{- \frac{5 x}{2}}{- 1}$

Step 1.1.3.2

Simplify the left side.

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Step 1.1.3.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} > \frac{3}{- 1} + \frac{- \frac{5 x}{2}}{- 1}$

Step 1.1.3.2.2

Divide $y$ by $1$ .

$y > \frac{3}{- 1} + \frac{- \frac{5 x}{2}}{- 1}$

Step 1.1.3.3

Simplify the right side.

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Step 1.1.3.3.1

Simplify each term.

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Step 1.1.3.3.1.1

Divide $3$ by $- 1$ .

$y > - 3 + \frac{- \frac{5 x}{2}}{- 1}$

Step 1.1.3.3.1.2

Dividing two negative values results in a positive value.

$y > - 3 + \frac{\frac{5 x}{2}}{1}$

Step 1.1.3.3.1.3

Divide $\frac{5 x}{2}$ by $1$ .

$y > - 3 + \frac{5 x}{2}$

Step 1.2

Rearrange terms.

$y > \frac{5 x}{2} - 3$

Step 1.3

Reorder terms.

$y > \frac{5}{2} x - 3$

Step 2

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

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Step 2.1

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

$m = \frac{5}{2}$

$b = - 3$

Step 2.2

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

Slope: $\frac{5}{2}$

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

Slope: $\frac{5}{2}$

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

Step 3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $\frac{5}{2} x - 3$ .

$y > \frac{5}{2} x - 3$

Step 4