Pre-Algebra Examples

$y - (- 5) = - \frac{7}{2} \cdot (x - (- 4))$

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

Multiply $- 1$ by $- 5$ .

$y + 5 = - \frac{7}{2} \cdot (x - (- 4))$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify $- \frac{7}{2} \cdot (x - (- 4))$ .

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Step 1.3.1.1

Simplify terms.

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Step 1.3.1.1.1

Multiply $- 1$ by $- 4$ .

$y + 5 = - \frac{7}{2} \cdot (x + 4)$

Step 1.3.1.1.2

Apply the distributive property.

$y + 5 = - \frac{7}{2} x - \frac{7}{2} \cdot 4$

Step 1.3.1.1.3

Combine $x$ and $\frac{7}{2}$ .

$y + 5 = - \frac{x \cdot 7}{2} - \frac{7}{2} \cdot 4$

Step 1.3.1.1.4

Cancel the common factor of $2$ .

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Step 1.3.1.1.4.1

Move the leading negative in $- \frac{7}{2}$ into the numerator.

$y + 5 = - \frac{x \cdot 7}{2} + \frac{- 7}{2} \cdot 4$

Step 1.3.1.1.4.2

Factor $2$ out of $4$ .

$y + 5 = - \frac{x \cdot 7}{2} + \frac{- 7}{2} \cdot (2 (2))$

Step 1.3.1.1.4.3

Cancel the common factor.

$y + 5 = - \frac{x \cdot 7}{2} + \frac{- 7}{2} \cdot (2 \cdot 2)$

Step 1.3.1.1.4.4

Rewrite the expression.

$y + 5 = - \frac{x \cdot 7}{2} - 7 \cdot 2$

Step 1.3.1.1.5

Multiply $- 7$ by $2$ .

$y + 5 = - \frac{x \cdot 7}{2} - 14$

Step 1.3.1.2

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

$y + 5 = - \frac{7 x}{2} - 14$

Step 1.4

Move all terms not containing $y$ to the right side of the equation.

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Step 1.4.1

Subtract $5$ from both sides of the equation.

$y = - \frac{7 x}{2} - 14 - 5$

Step 1.4.2

Subtract $5$ from $- 14$ .

$y = - \frac{7 x}{2} - 19$

Step 1.5

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

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Step 1.5.1

Reorder terms.

$y = - (\frac{7}{2} x) - 19$

Step 1.5.2

Remove parentheses.

$y = - \frac{7}{2} x - 19$

Step 2

Using the slope-intercept form, the slope is $- \frac{7}{2}$ .

$m = - \frac{7}{2}$

Step 3