Calculus Examples

$y + \frac{5}{4} = - \frac{5}{16} (x + 4)$

Step 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

Rewrite in slope-intercept form.

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Step 2.1

Simplify the right side.

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Step 2.1.1

Simplify $- \frac{5}{16} (x + 4)$ .

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Step 2.1.1.1

Simplify terms.

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Step 2.1.1.1.1

Apply the distributive property.

$y + \frac{5}{4} = - \frac{5}{16} x - \frac{5}{16} \cdot 4$

Step 2.1.1.1.2

Combine $x$ and $\frac{5}{16}$ .

$y + \frac{5}{4} = - \frac{x \cdot 5}{16} - \frac{5}{16} \cdot 4$

Step 2.1.1.1.3

Cancel the common factor of $4$ .

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Step 2.1.1.1.3.1

Move the leading negative in $- \frac{5}{16}$ into the numerator.

$y + \frac{5}{4} = - \frac{x \cdot 5}{16} + \frac{- 5}{16} \cdot 4$

Step 2.1.1.1.3.2

Factor $4$ out of $16$ .

$y + \frac{5}{4} = - \frac{x \cdot 5}{16} + \frac{- 5}{4 (4)} \cdot 4$

Step 2.1.1.1.3.3

Cancel the common factor.

$y + \frac{5}{4} = - \frac{x \cdot 5}{16} + \frac{- 5}{4 \cdot 4} \cdot 4$

Step 2.1.1.1.3.4

Rewrite the expression.

$y + \frac{5}{4} = - \frac{x \cdot 5}{16} + \frac{- 5}{4}$

Step 2.1.1.2

Simplify each term.

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Step 2.1.1.2.1

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

$y + \frac{5}{4} = - \frac{5 \cdot x}{16} + \frac{- 5}{4}$

Step 2.1.1.2.2

Move the negative in front of the fraction.

$y + \frac{5}{4} = - \frac{5 x}{16} - \frac{5}{4}$

Step 2.2

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

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Step 2.2.1

Subtract $\frac{5}{4}$ from both sides of the equation.

$y = - \frac{5 x}{16} - \frac{5}{4} - \frac{5}{4}$

Step 2.2.2

Combine the numerators over the common denominator.

$y = \frac{- 5 x}{16} + \frac{- 5 - 5}{4}$

Step 2.2.3

Subtract $5$ from $- 5$ .

$y = \frac{- 5 x}{16} + \frac{- 10}{4}$

Step 2.2.4

Simplify each term.

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Step 2.2.4.1

Move the negative in front of the fraction.

$y = - \frac{5 x}{16} + \frac{- 10}{4}$

Step 2.2.4.2

Cancel the common factor of $- 10$ and $4$ .

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Step 2.2.4.2.1

Factor $2$ out of $- 10$ .

$y = - \frac{5 x}{16} + \frac{2 (- 5)}{4}$

Step 2.2.4.2.2

Cancel the common factors.

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Step 2.2.4.2.2.1

Factor $2$ out of $4$ .

$y = - \frac{5 x}{16} + \frac{2 \cdot - 5}{2 \cdot 2}$

Step 2.2.4.2.2.2

Cancel the common factor.

$y = - \frac{5 x}{16} + \frac{2 \cdot - 5}{2 \cdot 2}$

Step 2.2.4.2.2.3

Rewrite the expression.

$y = - \frac{5 x}{16} + \frac{- 5}{2}$

Step 2.2.4.3

Move the negative in front of the fraction.

$y = - \frac{5 x}{16} - \frac{5}{2}$

Step 2.3

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

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Step 2.3.1

Reorder terms.

$y = - (\frac{5}{16} x) - \frac{5}{2}$

Step 2.3.2

Remove parentheses.

$y = - \frac{5}{16} x - \frac{5}{2}$