Pre-Algebra Examples

$\frac{3 y}{7} = - \frac{3}{5}$

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

Multiply both sides of the equation by $\frac{7}{3}$ .

$\frac{7}{3} \cdot \frac{3 y}{7} = \frac{7}{3} (- \frac{3}{5})$

Step 1.3

Simplify both sides of the equation.

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Step 1.3.1

Simplify the left side.

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Step 1.3.1.1

Simplify $\frac{7}{3} \cdot \frac{3 y}{7}$ .

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Step 1.3.1.1.1

Cancel the common factor of $7$ .

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Step 1.3.1.1.1.1

Cancel the common factor.

$\frac{7}{3} \cdot \frac{3 y}{7} = \frac{7}{3} (- \frac{3}{5})$

Step 1.3.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 y) = \frac{7}{3} (- \frac{3}{5})$

Step 1.3.1.1.2

Cancel the common factor of $3$ .

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Step 1.3.1.1.2.1

Factor $3$ out of $3 y$ .

$\frac{1}{3} (3 (y)) = \frac{7}{3} (- \frac{3}{5})$

Step 1.3.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 y) = \frac{7}{3} (- \frac{3}{5})$

Step 1.3.1.1.2.3

Rewrite the expression.

$y = \frac{7}{3} (- \frac{3}{5})$

Step 1.3.2

Simplify the right side.

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Step 1.3.2.1

Simplify $\frac{7}{3} (- \frac{3}{5})$ .

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Step 1.3.2.1.1

Cancel the common factor of $3$ .

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Step 1.3.2.1.1.1

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

$y = \frac{7}{3} \cdot \frac{- 3}{5}$

Step 1.3.2.1.1.2

Factor $3$ out of $- 3$ .

$y = \frac{7}{3} \cdot \frac{3 (- 1)}{5}$

Step 1.3.2.1.1.3

Cancel the common factor.

$y = \frac{7}{3} \cdot \frac{3 \cdot - 1}{5}$

Step 1.3.2.1.1.4

Rewrite the expression.

$y = 7 (\frac{- 1}{5})$

Step 1.3.2.1.2

Combine $7$ and $\frac{- 1}{5}$ .

$y = \frac{7 \cdot - 1}{5}$

Step 1.3.2.1.3

Simplify the expression.

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Step 1.3.2.1.3.1

Multiply $7$ by $- 1$ .

$y = \frac{- 7}{5}$

Step 1.3.2.1.3.2

Move the negative in front of the fraction.

$y = - \frac{7}{5}$

Step 2

Using the slope-intercept form, the y-intercept is $- \frac{7}{5}$ .

$b = - \frac{7}{5}$

Step 3

y-intercept in point form.

$(0, - \frac{7}{5})$

Step 4