Pre-Algebra Examples

$y - 6 = - \frac{2}{5} \cdot (x - 10)$

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 right side.

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Step 1.2.1

Simplify $- \frac{2}{5} \cdot (x - 10)$ .

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Step 1.2.1.1

Simplify terms.

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Step 1.2.1.1.1

Apply the distributive property.

$y - 6 = - \frac{2}{5} x - \frac{2}{5} \cdot - 10$

Step 1.2.1.1.2

Combine $x$ and $\frac{2}{5}$ .

$y - 6 = - \frac{x \cdot 2}{5} - \frac{2}{5} \cdot - 10$

Step 1.2.1.1.3

Cancel the common factor of $5$ .

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Step 1.2.1.1.3.1

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$y - 6 = - \frac{x \cdot 2}{5} + \frac{- 2}{5} \cdot - 10$

Step 1.2.1.1.3.2

Factor $5$ out of $- 10$ .

$y - 6 = - \frac{x \cdot 2}{5} + \frac{- 2}{5} \cdot (5 (- 2))$

Step 1.2.1.1.3.3

Cancel the common factor.

$y - 6 = - \frac{x \cdot 2}{5} + \frac{- 2}{5} \cdot (5 \cdot - 2)$

Step 1.2.1.1.3.4

Rewrite the expression.

$y - 6 = - \frac{x \cdot 2}{5} - 2 \cdot - 2$

Step 1.2.1.1.4

Multiply $- 2$ by $- 2$ .

$y - 6 = - \frac{x \cdot 2}{5} + 4$

Step 1.2.1.2

Move $2$ to the left of $x$ .

$y - 6 = - \frac{2 x}{5} + 4$

Step 1.3

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

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Step 1.3.1

Add $6$ to both sides of the equation.

$y = - \frac{2 x}{5} + 4 + 6$

Step 1.3.2

Add $4$ and $6$ .

$y = - \frac{2 x}{5} + 10$

Step 1.4

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

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Step 1.4.1

Reorder terms.

$y = - (\frac{2}{5} x) + 10$

Step 1.4.2

Remove parentheses.

$y = - \frac{2}{5} x + 10$

Step 2

Using the slope-intercept form, the y-intercept is $10$ .

$b = 10$

Step 3

y-intercept in point form.

$(0, 10)$

Step 4