Calculus Examples

$y - 1 = - \frac{11}{10} (x - 2)$

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 $- \frac{11}{10} (x - 2)$ .

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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.

$y - 1 = - \frac{11}{10} x - \frac{11}{10} \cdot - 2$

Step 2.1.1.1.2

Combine $x$ and $\frac{11}{10}$ .

$y - 1 = - \frac{x \cdot 11}{10} - \frac{11}{10} \cdot - 2$

Step 2.1.1.1.3

Cancel the common factor of $2$ .

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Step 2.1.1.1.3.1

Move the leading negative in $- \frac{11}{10}$ into the numerator.

$y - 1 = - \frac{x \cdot 11}{10} + \frac{- 11}{10} \cdot - 2$

Step 2.1.1.1.3.2

Factor $2$ out of $10$ .

$y - 1 = - \frac{x \cdot 11}{10} + \frac{- 11}{2 (5)} \cdot - 2$

Step 2.1.1.1.3.3

Factor $2$ out of $- 2$ .

$y - 1 = - \frac{x \cdot 11}{10} + \frac{- 11}{2 \cdot 5} \cdot (2 \cdot - 1)$

Step 2.1.1.1.3.4

Cancel the common factor.

$y - 1 = - \frac{x \cdot 11}{10} + \frac{- 11}{2 \cdot 5} \cdot (2 \cdot - 1)$

Step 2.1.1.1.3.5

Rewrite the expression.

$y - 1 = - \frac{x \cdot 11}{10} + \frac{- 11}{5} \cdot - 1$

Step 2.1.1.1.4

Combine $\frac{- 11}{5}$ and $- 1$ .

$y - 1 = - \frac{x \cdot 11}{10} + \frac{- 11 \cdot - 1}{5}$

Step 2.1.1.1.5

Multiply $- 11$ by $- 1$ .

$y - 1 = - \frac{x \cdot 11}{10} + \frac{11}{5}$

Step 2.1.1.2

Move $11$ to the left of $x$ .

$y - 1 = - \frac{11 x}{10} + \frac{11}{5}$

Step 2.2

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

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Step 2.2.1

Add $1$ to both sides of the equation.

$y = - \frac{11 x}{10} + \frac{11}{5} + 1$

Step 2.2.2

Write $1$ as a fraction with a common denominator.

$y = - \frac{11 x}{10} + \frac{11}{5} + \frac{5}{5}$

Step 2.2.3

Combine the numerators over the common denominator.

$y = - \frac{11 x}{10} + \frac{11 + 5}{5}$

Step 2.2.4

Add $11$ and $5$ .

$y = - \frac{11 x}{10} + \frac{16}{5}$

Step 2.3

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

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Step 2.3.1

Reorder terms.

$y = - (\frac{11}{10} x) + \frac{16}{5}$

Step 2.3.2

Remove parentheses.

$y = - \frac{11}{10} x + \frac{16}{5}$