Precalculus Examples

$4 (23 y - 4 x) = 14$

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 left side.

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Step 2.1.1

Simplify $4 (23 y - 4 x)$ .

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Step 2.1.1.1

Apply the distributive property.

$4 (23 y) + 4 (- 4 x) = 14$

Step 2.1.1.2

Multiply.

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Step 2.1.1.2.1

Multiply $23$ by $4$ .

$92 y + 4 (- 4 x) = 14$

Step 2.1.1.2.2

Multiply $- 4$ by $4$ .

$92 y - 16 x = 14$

Step 2.2

Add $16 x$ to both sides of the equation.

$92 y = 14 + 16 x$

Step 2.3

Divide each term in $92 y = 14 + 16 x$ by $92$ and simplify.

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Step 2.3.1

Divide each term in $92 y = 14 + 16 x$ by $92$ .

$\frac{92 y}{92} = \frac{14}{92} + \frac{16 x}{92}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $92$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{92 y}{92} = \frac{14}{92} + \frac{16 x}{92}$

Step 2.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{14}{92} + \frac{16 x}{92}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Simplify each term.

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Step 2.3.3.1.1

Cancel the common factor of $14$ and $92$ .

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Step 2.3.3.1.1.1

Factor $2$ out of $14$ .

$y = \frac{2 (7)}{92} + \frac{16 x}{92}$

Step 2.3.3.1.1.2

Cancel the common factors.

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Step 2.3.3.1.1.2.1

Factor $2$ out of $92$ .

$y = \frac{2 \cdot 7}{2 \cdot 46} + \frac{16 x}{92}$

Step 2.3.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot 7}{2 \cdot 46} + \frac{16 x}{92}$

Step 2.3.3.1.1.2.3

Rewrite the expression.

$y = \frac{7}{46} + \frac{16 x}{92}$

Step 2.3.3.1.2

Cancel the common factor of $16$ and $92$ .

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Step 2.3.3.1.2.1

Factor $4$ out of $16 x$ .

$y = \frac{7}{46} + \frac{4 (4 x)}{92}$

Step 2.3.3.1.2.2

Cancel the common factors.

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Step 2.3.3.1.2.2.1

Factor $4$ out of $92$ .

$y = \frac{7}{46} + \frac{4 (4 x)}{4 (23)}$

Step 2.3.3.1.2.2.2

Cancel the common factor.

$y = \frac{7}{46} + \frac{4 (4 x)}{4 \cdot 23}$

Step 2.3.3.1.2.2.3

Rewrite the expression.

$y = \frac{7}{46} + \frac{4 x}{23}$

Step 2.4

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

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Step 2.4.1

Reorder $\frac{7}{46}$ and $\frac{4 x}{23}$ .

$y = \frac{4 x}{23} + \frac{7}{46}$

Step 2.4.2

Reorder terms.

$y = \frac{4}{23} x + \frac{7}{46}$