Pre-Algebra Examples

$- \frac{8 y}{19} \div \frac{5}{8}$

Step 1

Solve for $y$ .

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Step 1.1

Rewrite the equation as $- \frac{64 y}{95} = x$ .

$- \frac{64 y}{95} = x$

Step 1.2

Multiply both sides of the equation by $- \frac{95}{64}$ .

$- \frac{95}{64} (- \frac{64 y}{95}) = - \frac{95}{64} x$

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 $- \frac{95}{64} (- \frac{64 y}{95})$ .

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Step 1.3.1.1.1

Cancel the common factor of $95$ .

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Step 1.3.1.1.1.1

Move the leading negative in $- \frac{95}{64}$ into the numerator.

$\frac{- 95}{64} (- \frac{64 y}{95}) = - \frac{95}{64} x$

Step 1.3.1.1.1.2

Move the leading negative in $- \frac{64 y}{95}$ into the numerator.

$\frac{- 95}{64} \cdot \frac{- 64 y}{95} = - \frac{95}{64} x$

Step 1.3.1.1.1.3

Factor $95$ out of $- 95$ .

$\frac{95 (- 1)}{64} \cdot \frac{- 64 y}{95} = - \frac{95}{64} x$

Step 1.3.1.1.1.4

Cancel the common factor.

$\frac{95 \cdot - 1}{64} \cdot \frac{- 64 y}{95} = - \frac{95}{64} x$

Step 1.3.1.1.1.5

Rewrite the expression.

$\frac{- 1}{64} (- 64 y) = - \frac{95}{64} x$

Step 1.3.1.1.2

Cancel the common factor of $64$ .

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Step 1.3.1.1.2.1

Factor $64$ out of $- 64 y$ .

$\frac{- 1}{64} (64 (- y)) = - \frac{95}{64} x$

Step 1.3.1.1.2.2

Cancel the common factor.

$\frac{- 1}{64} (64 (- y)) = - \frac{95}{64} x$

Step 1.3.1.1.2.3

Rewrite the expression.

$- - y = - \frac{95}{64} x$

Step 1.3.1.1.3

Multiply.

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Step 1.3.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{95}{64} x$

Step 1.3.1.1.3.2

Multiply $y$ by $1$ .

$y = - \frac{95}{64} x$

Step 1.3.2

Simplify the right side.

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Step 1.3.2.1

Simplify $- \frac{95}{64} x$ .

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Step 1.3.2.1.1

Combine $x$ and $\frac{95}{64}$ .

$y = - \frac{x \cdot 95}{64}$

Step 1.3.2.1.2

Move $95$ to the left of $x$ .

$y = - \frac{95 x}{64}$

Step 2

Rewrite in slope-intercept form.

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Step 2.1

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 2.2

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

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Step 2.2.1

Reorder terms.

$y = - (\frac{95}{64} x)$

Step 2.2.2

Remove parentheses.

$y = - \frac{95}{64} x$

Step 3

Use the slope-intercept form to find the slope and y-intercept.

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Step 3.1

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = - \frac{95}{64}$

$b = 0$

Step 3.2

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $- \frac{95}{64}$

y-intercept: $(0, 0)$

Slope: $- \frac{95}{64}$

y-intercept: $(0, 0)$

Step 4

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

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Step 4.1

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

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Step 4.1.1

Reorder terms.

$y = - (\frac{95}{64} x)$

Step 4.1.2

Remove parentheses.

$y = - \frac{95}{64} x$

Step 4.2

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ 0 & 0 \\ 64 & - 95 \end{array}$

Step 5

Graph the line using the slope and the y-intercept, or the points.

Slope: $- \frac{95}{64}$

y-intercept: $(0, 0)$

$\begin{array}{c} x & y \\ 0 & 0 \\ 64 & - 95 \end{array}$

Step 6