Calculus Examples

$y - 2 \sqrt{3} = - 4 (x - \frac{π}{3})$

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 $- 4 (x - \frac{π}{3})$ .

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Step 2.1.1.1

Apply the distributive property.

$y - 2 \sqrt{3} = - 4 x - 4 (- \frac{π}{3})$

Step 2.1.1.2

Multiply $- 4 (- \frac{π}{3})$ .

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Step 2.1.1.2.1

Multiply $- 1$ by $- 4$ .

$y - 2 \sqrt{3} = - 4 x + 4 \frac{π}{3}$

Step 2.1.1.2.2

Combine $4$ and $\frac{π}{3}$ .

$y - 2 \sqrt{3} = - 4 x + \frac{4 π}{3}$

Step 2.2

Add $2 \sqrt{3}$ to both sides of the equation.

$y = - 4 x + \frac{4 π}{3} + 2 \sqrt{3}$

Step 2.3

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

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Step 2.3.1

To write $2 \sqrt{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = - 4 x + \frac{4 π}{3} + 2 \sqrt{3} \cdot \frac{3}{3}$

Step 2.3.2

Combine $2 \sqrt{3}$ and $\frac{3}{3}$ .

$y = - 4 x + \frac{4 π}{3} + \frac{2 \sqrt{3} \cdot 3}{3}$

Step 2.3.3

Combine the numerators over the common denominator.

$y = - 4 x + \frac{4 π + 2 \sqrt{3} \cdot 3}{3}$

Step 2.3.4

Multiply $3$ by $2$ .

$y = - 4 x + \frac{4 π + 6 \sqrt{3}}{3}$