Calculus Examples

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

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 left side.

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Step 1.2.1

Factor $2$ out of $4 - 2 x$ .

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Step 1.2.1.1

Factor $2$ out of $4$ .

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

Step 1.2.1.2

Factor $2$ out of $- 2 x$ .

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

Step 1.2.1.3

Factor $2$ out of $2 (2) + 2 (- x)$ .

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

Step 1.3

Rewrite the equation as $y = \frac{2 (2 - x)}{3}$ .

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

Step 1.4

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

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Step 1.4.1

Apply the distributive property.

$y = \frac{2 \cdot 2 + 2 (- x)}{3}$

Step 1.4.2

Multiply $2$ by $2$ .

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

Step 1.4.3

Multiply $- 1$ by $2$ .

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

Step 1.4.4

Split the fraction $\frac{4 - 2 x}{3}$ into two fractions.

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

Step 1.4.5

Move the negative in front of the fraction.

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

Step 1.4.6

Rearrange terms.

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

Step 1.4.7

Reorder terms.

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

Step 1.4.8

Remove parentheses.

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

Step 2

Using the slope-intercept form, the slope is $- \frac{2}{3}$ .

$m = - \frac{2}{3}$

Step 3