Pre-Algebra Examples

$\frac{5}{2} x + \frac{2}{3} y - 5 = 0$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

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 1.2

Simplify the left side.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

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

$\frac{5 x}{2} + \frac{2}{3} y - 5 = 0$

Step 1.2.1.2

Combine $\frac{2}{3}$ and $y$ .

$\frac{5 x}{2} + \frac{2 y}{3} - 5 = 0$

Step 1.3

Move all terms not containing $y$ to the right side of the equation.

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Step 1.3.1

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

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

Step 1.3.2

Add $5$ to both sides of the equation.

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

Step 1.4

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} \cdot \frac{2 y}{3} = \frac{3}{2} (- \frac{5 x}{2} + 5)$

Step 1.5

Simplify both sides of the equation.

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Step 1.5.1

Simplify the left side.

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Step 1.5.1.1

Simplify $\frac{3}{2} \cdot \frac{2 y}{3}$ .

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Step 1.5.1.1.1

Cancel the common factor of $3$ .

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Step 1.5.1.1.1.1

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 y}{3} = \frac{3}{2} (- \frac{5 x}{2} + 5)$

Step 1.5.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 y) = \frac{3}{2} (- \frac{5 x}{2} + 5)$

Step 1.5.1.1.2

Cancel the common factor of $2$ .

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Step 1.5.1.1.2.1

Factor $2$ out of $2 y$ .

$\frac{1}{2} (2 (y)) = \frac{3}{2} (- \frac{5 x}{2} + 5)$

Step 1.5.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 y) = \frac{3}{2} (- \frac{5 x}{2} + 5)$

Step 1.5.1.1.2.3

Rewrite the expression.

$y = \frac{3}{2} (- \frac{5 x}{2} + 5)$

Step 1.5.2

Simplify the right side.

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Step 1.5.2.1

Simplify $\frac{3}{2} (- \frac{5 x}{2} + 5)$ .

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Step 1.5.2.1.1

Apply the distributive property.

$y = \frac{3}{2} (- \frac{5 x}{2}) + \frac{3}{2} \cdot 5$

Step 1.5.2.1.2

Multiply $\frac{3}{2} (- \frac{5 x}{2})$ .

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Step 1.5.2.1.2.1

Multiply $\frac{3}{2}$ by $\frac{5 x}{2}$ .

$y = - \frac{3 (5 x)}{2 \cdot 2} + \frac{3}{2} \cdot 5$

Step 1.5.2.1.2.2

Multiply $5$ by $3$ .

$y = - \frac{15 x}{2 \cdot 2} + \frac{3}{2} \cdot 5$

Step 1.5.2.1.2.3

Multiply $2$ by $2$ .

$y = - \frac{15 x}{4} + \frac{3}{2} \cdot 5$

Step 1.5.2.1.3

Multiply $\frac{3}{2} \cdot 5$ .

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Step 1.5.2.1.3.1

Combine $\frac{3}{2}$ and $5$ .

$y = - \frac{15 x}{4} + \frac{3 \cdot 5}{2}$

Step 1.5.2.1.3.2

Multiply $3$ by $5$ .

$y = - \frac{15 x}{4} + \frac{15}{2}$

Step 1.6

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

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Step 1.6.1

Reorder terms.

$y = - (\frac{15}{4} x) + \frac{15}{2}$

Step 1.6.2

Remove parentheses.

$y = - \frac{15}{4} x + \frac{15}{2}$

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 $y = m x + b$ .

$m = - \frac{15}{4}$

$b = \frac{15}{2}$

Step 2.2

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

Slope: $- \frac{15}{4}$

y-intercept: $(0, \frac{15}{2})$

Slope: $- \frac{15}{4}$

y-intercept: $(0, \frac{15}{2})$

Step 3