Algebra Examples

$6 x + 10 y = 8$

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

Subtract $6 x$ from both sides of the equation.

$10 y = 8 - 6 x$

Step 1.3

Divide each term in $10 y = 8 - 6 x$ by $10$ and simplify.

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Step 1.3.1

Divide each term in $10 y = 8 - 6 x$ by $10$ .

$\frac{10 y}{10} = \frac{8}{10} + \frac{- 6 x}{10}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $10$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{10 y}{10} = \frac{8}{10} + \frac{- 6 x}{10}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{8}{10} + \frac{- 6 x}{10}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Cancel the common factor of $8$ and $10$ .

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Step 1.3.3.1.1.1

Factor $2$ out of $8$ .

$y = \frac{2 (4)}{10} + \frac{- 6 x}{10}$

Step 1.3.3.1.1.2

Cancel the common factors.

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Step 1.3.3.1.1.2.1

Factor $2$ out of $10$ .

$y = \frac{2 \cdot 4}{2 \cdot 5} + \frac{- 6 x}{10}$

Step 1.3.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot 4}{2 \cdot 5} + \frac{- 6 x}{10}$

Step 1.3.3.1.1.2.3

Rewrite the expression.

$y = \frac{4}{5} + \frac{- 6 x}{10}$

Step 1.3.3.1.2

Cancel the common factor of $- 6$ and $10$ .

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Step 1.3.3.1.2.1

Factor $2$ out of $- 6 x$ .

$y = \frac{4}{5} + \frac{2 (- 3 x)}{10}$

Step 1.3.3.1.2.2

Cancel the common factors.

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Step 1.3.3.1.2.2.1

Factor $2$ out of $10$ .

$y = \frac{4}{5} + \frac{2 (- 3 x)}{2 (5)}$

Step 1.3.3.1.2.2.2

Cancel the common factor.

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

Step 1.3.3.1.2.2.3

Rewrite the expression.

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

Step 1.3.3.1.3

Move the negative in front of the fraction.

$y = \frac{4}{5} - \frac{3 x}{5}$

Step 1.4

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

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Step 1.4.1

Reorder $\frac{4}{5}$ and $- \frac{3 x}{5}$ .

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

Step 1.4.2

Reorder terms.

$y = - (\frac{3}{5} x) + \frac{4}{5}$

Step 1.4.3

Remove parentheses.

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

Step 2

Using the slope-intercept form, the slope is $- \frac{3}{5}$ .

$m = - \frac{3}{5}$

Step 3