Pre-Algebra Examples

$\frac{3}{5} x - 2 y = 5$

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

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

$\frac{3 x}{5} - 2 y = 5$

Step 1.3

Subtract $\frac{3 x}{5}$ from both sides of the equation.

$- 2 y = 5 - \frac{3 x}{5}$

Step 1.4

Divide each term in $- 2 y = 5 - \frac{3 x}{5}$ by $- 2$ and simplify.

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Step 1.4.1

Divide each term in $- 2 y = 5 - \frac{3 x}{5}$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{5}{- 2} + \frac{- \frac{3 x}{5}}{- 2}$

Step 1.4.2

Simplify the left side.

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Step 1.4.2.1

Cancel the common factor of $- 2$ .

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Step 1.4.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{5}{- 2} + \frac{- \frac{3 x}{5}}{- 2}$

Step 1.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{5}{- 2} + \frac{- \frac{3 x}{5}}{- 2}$

Step 1.4.3

Simplify the right side.

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Step 1.4.3.1

Simplify each term.

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Step 1.4.3.1.1

Move the negative in front of the fraction.

$y = - \frac{5}{2} + \frac{- \frac{3 x}{5}}{- 2}$

Step 1.4.3.1.2

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{5}{2} - \frac{3 x}{5} \cdot \frac{1}{- 2}$

Step 1.4.3.1.3

Move the negative in front of the fraction.

$y = - \frac{5}{2} - \frac{3 x}{5} (- \frac{1}{2})$

Step 1.4.3.1.4

Multiply $- \frac{3 x}{5} (- \frac{1}{2})$ .

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Step 1.4.3.1.4.1

Multiply $- 1$ by $- 1$ .

$y = - \frac{5}{2} + 1 \frac{3 x}{5} \frac{1}{2}$

Step 1.4.3.1.4.2

Multiply $\frac{3 x}{5}$ by $1$ .

$y = - \frac{5}{2} + \frac{3 x}{5} \cdot \frac{1}{2}$

Step 1.4.3.1.4.3

Multiply $\frac{3 x}{5}$ by $\frac{1}{2}$ .

$y = - \frac{5}{2} + \frac{3 x}{5 \cdot 2}$

Step 1.4.3.1.4.4

Multiply $5$ by $2$ .

$y = - \frac{5}{2} + \frac{3 x}{10}$

Step 1.5

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

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Step 1.5.1

Reorder $- \frac{5}{2}$ and $\frac{3 x}{10}$ .

$y = \frac{3 x}{10} - \frac{5}{2}$

Step 1.5.2

Reorder terms.

$y = \frac{3}{10} x - \frac{5}{2}$

Step 2

Using the slope-intercept form, the y-intercept is $- \frac{5}{2}$ .

$b = - \frac{5}{2}$

Step 3

y-intercept in point form.

$(0, - \frac{5}{2})$

Step 4