Pre-Algebra Examples

$- \frac{9}{5} x + \frac{3}{5} y = 2$

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 $x$ and $\frac{9}{5}$ .

$- \frac{x \cdot 9}{5} + \frac{3}{5} y = 2$

Step 1.2.1.2

Move $9$ to the left of $x$ .

$- \frac{9 \cdot x}{5} + \frac{3}{5} y = 2$

Step 1.2.1.3

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

$- \frac{9 x}{5} + \frac{3 y}{5} = 2$

Step 1.3

Add $\frac{9 x}{5}$ to both sides of the equation.

$\frac{3 y}{5} = 2 + \frac{9 x}{5}$

Step 1.4

Multiply both sides of the equation by $\frac{5}{3}$ .

$\frac{5}{3} \cdot \frac{3 y}{5} = \frac{5}{3} (2 + \frac{9 x}{5})$

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 $\frac{5}{3} \cdot \frac{3 y}{5}$ .

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Step 1.5.1.1.1

Cancel the common factor of $5$ .

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Step 1.5.1.1.1.1

Cancel the common factor.

$\frac{5}{3} \cdot \frac{3 y}{5} = \frac{5}{3} (2 + \frac{9 x}{5})$

Step 1.5.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 y) = \frac{5}{3} (2 + \frac{9 x}{5})$

Step 1.5.1.1.2

Cancel the common factor of $3$ .

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Step 1.5.1.1.2.1

Factor $3$ out of $3 y$ .

$\frac{1}{3} (3 (y)) = \frac{5}{3} (2 + \frac{9 x}{5})$

Step 1.5.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 y) = \frac{5}{3} (2 + \frac{9 x}{5})$

Step 1.5.1.1.2.3

Rewrite the expression.

$y = \frac{5}{3} (2 + \frac{9 x}{5})$

Step 1.5.2

Simplify the right side.

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Step 1.5.2.1

Simplify $\frac{5}{3} (2 + \frac{9 x}{5})$ .

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Step 1.5.2.1.1

Apply the distributive property.

$y = \frac{5}{3} \cdot 2 + \frac{5}{3} \cdot \frac{9 x}{5}$

Step 1.5.2.1.2

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

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Step 1.5.2.1.2.1

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

$y = \frac{5 \cdot 2}{3} + \frac{5}{3} \cdot \frac{9 x}{5}$

Step 1.5.2.1.2.2

Multiply $5$ by $2$ .

$y = \frac{10}{3} + \frac{5}{3} \cdot \frac{9 x}{5}$

Step 1.5.2.1.3

Cancel the common factor of $5$ .

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Step 1.5.2.1.3.1

Cancel the common factor.

$y = \frac{10}{3} + \frac{5}{3} \cdot \frac{9 x}{5}$

Step 1.5.2.1.3.2

Rewrite the expression.

$y = \frac{10}{3} + \frac{1}{3} (9 x)$

Step 1.5.2.1.4

Cancel the common factor of $3$ .

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Step 1.5.2.1.4.1

Factor $3$ out of $9 x$ .

$y = \frac{10}{3} + \frac{1}{3} (3 (3 x))$

Step 1.5.2.1.4.2

Cancel the common factor.

$y = \frac{10}{3} + \frac{1}{3} (3 (3 x))$

Step 1.5.2.1.4.3

Rewrite the expression.

$y = \frac{10}{3} + 3 x$

Step 1.6

Reorder $\frac{10}{3}$ and $3 x$ .

$y = 3 x + \frac{10}{3}$

Step 2

Using the slope-intercept form, the slope is $3$ .

$m = 3$

Step 3