Calculus Examples

$y - \frac{1}{10} = \frac{3}{50} (x + 3)$

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 $\frac{3}{50} (x + 3)$ .

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Step 2.1.1.1

Apply the distributive property.

$y - \frac{1}{10} = \frac{3}{50} x + \frac{3}{50} \cdot 3$

Step 2.1.1.2

Combine $\frac{3}{50}$ and $x$ .

$y - \frac{1}{10} = \frac{3 x}{50} + \frac{3}{50} \cdot 3$

Step 2.1.1.3

Multiply $\frac{3}{50} \cdot 3$ .

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Step 2.1.1.3.1

Combine $\frac{3}{50}$ and $3$ .

$y - \frac{1}{10} = \frac{3 x}{50} + \frac{3 \cdot 3}{50}$

Step 2.1.1.3.2

Multiply $3$ by $3$ .

$y - \frac{1}{10} = \frac{3 x}{50} + \frac{9}{50}$

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 $\frac{1}{10}$ to both sides of the equation.

$y = \frac{3 x}{50} + \frac{9}{50} + \frac{1}{10}$

Step 2.2.2

To write $\frac{1}{10}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = \frac{3 x}{50} + \frac{9}{50} + \frac{1}{10} \cdot \frac{5}{5}$

Step 2.2.3

Write each expression with a common denominator of $50$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.3.1

Multiply $\frac{1}{10}$ by $\frac{5}{5}$ .

$y = \frac{3 x}{50} + \frac{9}{50} + \frac{5}{10 \cdot 5}$

Step 2.2.3.2

Multiply $10$ by $5$ .

$y = \frac{3 x}{50} + \frac{9}{50} + \frac{5}{50}$

Step 2.2.4

Combine the numerators over the common denominator.

$y = \frac{3 x}{50} + \frac{9 + 5}{50}$

Step 2.2.5

Add $9$ and $5$ .

$y = \frac{3 x}{50} + \frac{14}{50}$

Step 2.2.6

Cancel the common factor of $14$ and $50$ .

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Step 2.2.6.1

Factor $2$ out of $14$ .

$y = \frac{3 x}{50} + \frac{2 (7)}{50}$

Step 2.2.6.2

Cancel the common factors.

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Step 2.2.6.2.1

Factor $2$ out of $50$ .

$y = \frac{3 x}{50} + \frac{2 \cdot 7}{2 \cdot 25}$

Step 2.2.6.2.2

Cancel the common factor.

$y = \frac{3 x}{50} + \frac{2 \cdot 7}{2 \cdot 25}$

Step 2.2.6.2.3

Rewrite the expression.

$y = \frac{3 x}{50} + \frac{7}{25}$

Step 2.3

Reorder terms.

$y = \frac{3}{50} x + \frac{7}{25}$