Calculus Examples

$y - \frac{7}{2} = - \frac{7}{16} (x - 4)$

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 $- \frac{7}{16} (x - 4)$ .

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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.

$y - \frac{7}{2} = - \frac{7}{16} x - \frac{7}{16} \cdot - 4$

Step 2.1.1.1.2

Combine $x$ and $\frac{7}{16}$ .

$y - \frac{7}{2} = - \frac{x \cdot 7}{16} - \frac{7}{16} \cdot - 4$

Step 2.1.1.1.3

Cancel the common factor of $4$ .

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Step 2.1.1.1.3.1

Move the leading negative in $- \frac{7}{16}$ into the numerator.

$y - \frac{7}{2} = - \frac{x \cdot 7}{16} + \frac{- 7}{16} \cdot - 4$

Step 2.1.1.1.3.2

Factor $4$ out of $16$ .

$y - \frac{7}{2} = - \frac{x \cdot 7}{16} + \frac{- 7}{4 (4)} \cdot - 4$

Step 2.1.1.1.3.3

Factor $4$ out of $- 4$ .

$y - \frac{7}{2} = - \frac{x \cdot 7}{16} + \frac{- 7}{4 \cdot 4} \cdot (4 \cdot - 1)$

Step 2.1.1.1.3.4

Cancel the common factor.

$y - \frac{7}{2} = - \frac{x \cdot 7}{16} + \frac{- 7}{4 \cdot 4} \cdot (4 \cdot - 1)$

Step 2.1.1.1.3.5

Rewrite the expression.

$y - \frac{7}{2} = - \frac{x \cdot 7}{16} + \frac{- 7}{4} \cdot - 1$

Step 2.1.1.1.4

Combine $\frac{- 7}{4}$ and $- 1$ .

$y - \frac{7}{2} = - \frac{x \cdot 7}{16} + \frac{- 7 \cdot - 1}{4}$

Step 2.1.1.1.5

Multiply $- 7$ by $- 1$ .

$y - \frac{7}{2} = - \frac{x \cdot 7}{16} + \frac{7}{4}$

Step 2.1.1.2

Move $7$ to the left of $x$ .

$y - \frac{7}{2} = - \frac{7 x}{16} + \frac{7}{4}$

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 $\frac{7}{2}$ to both sides of the equation.

$y = - \frac{7 x}{16} + \frac{7}{4} + \frac{7}{2}$

Step 2.2.2

To write $\frac{7}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = - \frac{7 x}{16} + \frac{7}{4} + \frac{7}{2} \cdot \frac{2}{2}$

Step 2.2.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.3.1

Multiply $\frac{7}{2}$ by $\frac{2}{2}$ .

$y = - \frac{7 x}{16} + \frac{7}{4} + \frac{7 \cdot 2}{2 \cdot 2}$

Step 2.2.3.2

Multiply $2$ by $2$ .

$y = - \frac{7 x}{16} + \frac{7}{4} + \frac{7 \cdot 2}{4}$

Step 2.2.4

Combine the numerators over the common denominator.

$y = - \frac{7 x}{16} + \frac{7 + 7 \cdot 2}{4}$

Step 2.2.5

Simplify the numerator.

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Step 2.2.5.1

Multiply $7$ by $2$ .

$y = - \frac{7 x}{16} + \frac{7 + 14}{4}$

Step 2.2.5.2

Add $7$ and $14$ .

$y = - \frac{7 x}{16} + \frac{21}{4}$

Step 2.3

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

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Step 2.3.1

Reorder terms.

$y = - (\frac{7}{16} x) + \frac{21}{4}$

Step 2.3.2

Remove parentheses.

$y = - \frac{7}{16} x + \frac{21}{4}$