Algebra Examples

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

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 right side.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Combine $y$ and $\frac{4}{5}$ .

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

Step 1.2.1.2

Move $4$ to the left of $y$ .

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

Step 1.3

Rewrite the equation as $- \frac{4 y}{5} + 2 = x$ .

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

Step 1.4

Subtract $2$ from both sides of the equation.

$- \frac{4 y}{5} = x - 2$

Step 1.5

Multiply both sides of the equation by $- \frac{5}{4}$ .

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

Step 1.6

Simplify both sides of the equation.

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Step 1.6.1

Simplify the left side.

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Step 1.6.1.1

Simplify $- \frac{5}{4} (- \frac{4 y}{5})$ .

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Step 1.6.1.1.1

Cancel the common factor of $5$ .

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Step 1.6.1.1.1.1

Move the leading negative in $- \frac{5}{4}$ into the numerator.

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

Step 1.6.1.1.1.2

Move the leading negative in $- \frac{4 y}{5}$ into the numerator.

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

Step 1.6.1.1.1.3

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{4} \cdot \frac{- 4 y}{5} = - \frac{5}{4} (x - 2)$

Step 1.6.1.1.1.4

Cancel the common factor.

$\frac{5 \cdot - 1}{4} \cdot \frac{- 4 y}{5} = - \frac{5}{4} (x - 2)$

Step 1.6.1.1.1.5

Rewrite the expression.

$\frac{- 1}{4} (- 4 y) = - \frac{5}{4} (x - 2)$

Step 1.6.1.1.2

Cancel the common factor of $4$ .

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Step 1.6.1.1.2.1

Factor $4$ out of $- 4 y$ .

$\frac{- 1}{4} (4 (- y)) = - \frac{5}{4} (x - 2)$

Step 1.6.1.1.2.2

Cancel the common factor.

$\frac{- 1}{4} (4 (- y)) = - \frac{5}{4} (x - 2)$

Step 1.6.1.1.2.3

Rewrite the expression.

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

Step 1.6.1.1.3

Multiply.

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Step 1.6.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{5}{4} (x - 2)$

Step 1.6.1.1.3.2

Multiply $y$ by $1$ .

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

Step 1.6.2

Simplify the right side.

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Step 1.6.2.1

Simplify $- \frac{5}{4} (x - 2)$ .

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Step 1.6.2.1.1

Simplify terms.

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Step 1.6.2.1.1.1

Apply the distributive property.

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

Step 1.6.2.1.1.2

Combine $x$ and $\frac{5}{4}$ .

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

Step 1.6.2.1.1.3

Cancel the common factor of $2$ .

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Step 1.6.2.1.1.3.1

Move the leading negative in $- \frac{5}{4}$ into the numerator.

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

Step 1.6.2.1.1.3.2

Factor $2$ out of $4$ .

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

Step 1.6.2.1.1.3.3

Factor $2$ out of $- 2$ .

$y = - \frac{x \cdot 5}{4} + \frac{- 5}{2 \cdot 2} \cdot (2 \cdot - 1)$

Step 1.6.2.1.1.3.4

Cancel the common factor.

$y = - \frac{x \cdot 5}{4} + \frac{- 5}{2 \cdot 2} \cdot (2 \cdot - 1)$

Step 1.6.2.1.1.3.5

Rewrite the expression.

$y = - \frac{x \cdot 5}{4} + \frac{- 5}{2} \cdot - 1$

Step 1.6.2.1.1.4

Combine $\frac{- 5}{2}$ and $- 1$ .

$y = - \frac{x \cdot 5}{4} + \frac{- 5 \cdot - 1}{2}$

Step 1.6.2.1.1.5

Multiply $- 5$ by $- 1$ .

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

Step 1.6.2.1.2

Move $5$ to the left of $x$ .

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

Step 1.7

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

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Step 1.7.1

Reorder terms.

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

Step 1.7.2

Remove parentheses.

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

Step 2

Using the slope-intercept form, the y-intercept is $\frac{5}{2}$ .

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

Step 3

y-intercept in point form.

$(0, \frac{5}{2})$

Step 4