Calculus Examples

$y = 7 - \frac{9}{17} (x - 5)$

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 $7 - \frac{9}{17} (x - 5)$ .

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Step 2.1.1.1

Simplify each term.

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Step 2.1.1.1.1

Apply the distributive property.

$y = 7 - \frac{9}{17} x - \frac{9}{17} \cdot - 5$

Step 2.1.1.1.2

Combine $x$ and $\frac{9}{17}$ .

$y = 7 - \frac{x \cdot 9}{17} - \frac{9}{17} \cdot - 5$

Step 2.1.1.1.3

Multiply $- \frac{9}{17} \cdot - 5$ .

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Step 2.1.1.1.3.1

Multiply $- 5$ by $- 1$ .

$y = 7 - \frac{x \cdot 9}{17} + 5 (\frac{9}{17})$

Step 2.1.1.1.3.2

Combine $5$ and $\frac{9}{17}$ .

$y = 7 - \frac{x \cdot 9}{17} + \frac{5 \cdot 9}{17}$

Step 2.1.1.1.3.3

Multiply $5$ by $9$ .

$y = 7 - \frac{x \cdot 9}{17} + \frac{45}{17}$

Step 2.1.1.1.4

Move $9$ to the left of $x$ .

$y = 7 - \frac{9 x}{17} + \frac{45}{17}$

Step 2.1.1.2

To write $7$ as a fraction with a common denominator, multiply by $\frac{17}{17}$ .

$y = - \frac{9 x}{17} + 7 \cdot \frac{17}{17} + \frac{45}{17}$

Step 2.1.1.3

Combine $7$ and $\frac{17}{17}$ .

$y = - \frac{9 x}{17} + \frac{7 \cdot 17}{17} + \frac{45}{17}$

Step 2.1.1.4

Combine the numerators over the common denominator.

$y = - \frac{9 x}{17} + \frac{7 \cdot 17 + 45}{17}$

Step 2.1.1.5

Simplify the numerator.

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Step 2.1.1.5.1

Multiply $7$ by $17$ .

$y = - \frac{9 x}{17} + \frac{119 + 45}{17}$

Step 2.1.1.5.2

Add $119$ and $45$ .

$y = - \frac{9 x}{17} + \frac{164}{17}$

Step 2.2

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

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Step 2.2.1

Reorder terms.

$y = - (\frac{9}{17} x) + \frac{164}{17}$

Step 2.2.2

Remove parentheses.

$y = - \frac{9}{17} x + \frac{164}{17}$