Pre-Algebra Examples

$y - 4 = - \frac{3}{5} \cdot (x - 4)$

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 right side.

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Step 1.2.1

Simplify $- \frac{3}{5} \cdot (x - 4)$ .

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Step 1.2.1.1

Apply the distributive property.

$y - 4 = - \frac{3}{5} x - \frac{3}{5} \cdot - 4$

Step 1.2.1.2

Combine $x$ and $\frac{3}{5}$ .

$y - 4 = - \frac{x \cdot 3}{5} - \frac{3}{5} \cdot - 4$

Step 1.2.1.3

Multiply $- \frac{3}{5} \cdot - 4$ .

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Step 1.2.1.3.1

Multiply $- 4$ by $- 1$ .

$y - 4 = - \frac{x \cdot 3}{5} + 4 (\frac{3}{5})$

Step 1.2.1.3.2

Combine $4$ and $\frac{3}{5}$ .

$y - 4 = - \frac{x \cdot 3}{5} + \frac{4 \cdot 3}{5}$

Step 1.2.1.3.3

Multiply $4$ by $3$ .

$y - 4 = - \frac{x \cdot 3}{5} + \frac{12}{5}$

Step 1.2.1.4

Move $3$ to the left of $x$ .

$y - 4 = - \frac{3 x}{5} + \frac{12}{5}$

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 $4$ to both sides of the equation.

$y = - \frac{3 x}{5} + \frac{12}{5} + 4$

Step 1.3.2

To write $4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = - \frac{3 x}{5} + \frac{12}{5} + 4 \cdot \frac{5}{5}$

Step 1.3.3

Combine $4$ and $\frac{5}{5}$ .

$y = - \frac{3 x}{5} + \frac{12}{5} + \frac{4 \cdot 5}{5}$

Step 1.3.4

Combine the numerators over the common denominator.

$y = - \frac{3 x}{5} + \frac{12 + 4 \cdot 5}{5}$

Step 1.3.5

Simplify the numerator.

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Step 1.3.5.1

Multiply $4$ by $5$ .

$y = - \frac{3 x}{5} + \frac{12 + 20}{5}$

Step 1.3.5.2

Add $12$ and $20$ .

$y = - \frac{3 x}{5} + \frac{32}{5}$

Step 1.4

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

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Step 1.4.1

Reorder terms.

$y = - (\frac{3}{5} x) + \frac{32}{5}$

Step 1.4.2

Remove parentheses.

$y = - \frac{3}{5} x + \frac{32}{5}$

Step 2

Using the slope-intercept form, the y-intercept is $\frac{32}{5}$ .

$b = \frac{32}{5}$

Step 3

y-intercept in point form.

$(0, \frac{32}{5})$

Step 4