Pre-Algebra Examples

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

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

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

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Step 1.2.1

Subtract $\frac{2}{5}$ from both sides of the equation.

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.2.3

Subtract $2$ from $- 1$ .

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

Step 1.2.4

Move the negative in front of the fraction.

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $3$ .

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Step 1.3.2.1.1

Cancel the common factor.

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

Step 1.3.2.1.2

Divide $y$ by $1$ .

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

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 1.3.3.2

Cancel the common factor of $3$ .

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Step 1.3.3.2.1

Move the leading negative in $- \frac{3}{5}$ into the numerator.

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

Step 1.3.3.2.2

Factor $3$ out of $- 3$ .

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

Step 1.3.3.2.3

Cancel the common factor.

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

Step 1.3.3.2.4

Rewrite the expression.

$y = \frac{- 1}{5}$

Step 1.3.3.3

Move the negative in front of the fraction.

$y = - \frac{1}{5}$

Step 2

Using the slope-intercept form, the y-intercept is $- \frac{1}{5}$ .

$b = - \frac{1}{5}$

Step 3

y-intercept in point form.

$(0, - \frac{1}{5})$

Step 4