Pre-Algebra Examples

$5 x + 5 y < 25$

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

Subtract $5 x$ from both sides of the inequality.

$5 y < 25 - 5 x$

Step 1.1.2

Divide each term in $5 y < 25 - 5 x$ by $5$ and simplify.

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Step 1.1.2.1

Divide each term in $5 y < 25 - 5 x$ by $5$ .

$\frac{5 y}{5} < \frac{25}{5} + \frac{- 5 x}{5}$

Step 1.1.2.2

Simplify the left side.

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Step 1.1.2.2.1

Cancel the common factor of $5$ .

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Step 1.1.2.2.1.1

Cancel the common factor.

$\frac{5 y}{5} < \frac{25}{5} + \frac{- 5 x}{5}$

Step 1.1.2.2.1.2

Divide $y$ by $1$ .

$y < \frac{25}{5} + \frac{- 5 x}{5}$

Step 1.1.2.3

Simplify the right side.

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Step 1.1.2.3.1

Simplify each term.

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Step 1.1.2.3.1.1

Divide $25$ by $5$ .

$y < 5 + \frac{- 5 x}{5}$

Step 1.1.2.3.1.2

Cancel the common factor of $- 5$ and $5$ .

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Step 1.1.2.3.1.2.1

Factor $5$ out of $- 5 x$ .

$y < 5 + \frac{5 (- x)}{5}$

Step 1.1.2.3.1.2.2

Cancel the common factors.

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Step 1.1.2.3.1.2.2.1

Factor $5$ out of $5$ .

$y < 5 + \frac{5 (- x)}{5 (1)}$

Step 1.1.2.3.1.2.2.2

Cancel the common factor.

$y < 5 + \frac{5 (- x)}{5 \cdot 1}$

Step 1.1.2.3.1.2.2.3

Rewrite the expression.

$y < 5 + \frac{- x}{1}$

Step 1.1.2.3.1.2.2.4

Divide $- x$ by $1$ .

$y < 5 - x$

Step 1.2

Rearrange terms.

$y < - x + 5$

Step 2

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

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Step 2.1

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

$y = m x + b$

Step 2.2

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

$m = - 1$

$b = 5$

Step 2.3

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

Slope: $- 1$

y-intercept: $(0, 5)$

Slope: $- 1$

y-intercept: $(0, 5)$

Step 3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $- x + 5$ .

$y < - x + 5$

Step 4