Pre-Algebra Examples

$\frac{1}{7} x - \frac{3}{7} y - \frac{3}{11} x + \frac{6}{17} y$

Step 1

Solve for $y$ .

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Step 1.1

Add $\frac{10 x}{77}$ to both sides of the equation.

$- \frac{9 y}{119} = \frac{10 x}{77}$

Step 1.2

Multiply both sides of the equation by $- \frac{119}{9}$ .

$- \frac{119}{9} (- \frac{9 y}{119}) = - \frac{119}{9} \cdot \frac{10 x}{77}$

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 $- \frac{119}{9} (- \frac{9 y}{119})$ .

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Step 1.3.1.1.1

Cancel the common factor of $119$ .

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Step 1.3.1.1.1.1

Move the leading negative in $- \frac{119}{9}$ into the numerator.

$\frac{- 119}{9} (- \frac{9 y}{119}) = - \frac{119}{9} \cdot \frac{10 x}{77}$

Step 1.3.1.1.1.2

Move the leading negative in $- \frac{9 y}{119}$ into the numerator.

$\frac{- 119}{9} \cdot \frac{- 9 y}{119} = - \frac{119}{9} \cdot \frac{10 x}{77}$

Step 1.3.1.1.1.3

Factor $119$ out of $- 119$ .

$\frac{119 (- 1)}{9} \cdot \frac{- 9 y}{119} = - \frac{119}{9} \cdot \frac{10 x}{77}$

Step 1.3.1.1.1.4

Cancel the common factor.

$\frac{119 \cdot - 1}{9} \cdot \frac{- 9 y}{119} = - \frac{119}{9} \cdot \frac{10 x}{77}$

Step 1.3.1.1.1.5

Rewrite the expression.

$\frac{- 1}{9} (- 9 y) = - \frac{119}{9} \cdot \frac{10 x}{77}$

Step 1.3.1.1.2

Cancel the common factor of $9$ .

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Step 1.3.1.1.2.1

Factor $9$ out of $- 9 y$ .

$\frac{- 1}{9} (9 (- y)) = - \frac{119}{9} \cdot \frac{10 x}{77}$

Step 1.3.1.1.2.2

Cancel the common factor.

$\frac{- 1}{9} (9 (- y)) = - \frac{119}{9} \cdot \frac{10 x}{77}$

Step 1.3.1.1.2.3

Rewrite the expression.

$- - y = - \frac{119}{9} \cdot \frac{10 x}{77}$

Step 1.3.1.1.3

Multiply.

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Step 1.3.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{119}{9} \cdot \frac{10 x}{77}$

Step 1.3.1.1.3.2

Multiply $y$ by $1$ .

$y = - \frac{119}{9} \cdot \frac{10 x}{77}$

Step 1.3.2

Simplify the right side.

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Step 1.3.2.1

Simplify $- \frac{119}{9} \cdot \frac{10 x}{77}$ .

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Step 1.3.2.1.1

Cancel the common factor of $7$ .

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Step 1.3.2.1.1.1

Move the leading negative in $- \frac{119}{9}$ into the numerator.

$y = \frac{- 119}{9} \cdot \frac{10 x}{77}$

Step 1.3.2.1.1.2

Factor $7$ out of $- 119$ .

$y = \frac{7 (- 17)}{9} \cdot \frac{10 x}{77}$

Step 1.3.2.1.1.3

Factor $7$ out of $77$ .

$y = \frac{7 \cdot - 17}{9} \cdot \frac{10 x}{7 \cdot 11}$

Step 1.3.2.1.1.4

Cancel the common factor.

$y = \frac{7 \cdot - 17}{9} \cdot \frac{10 x}{7 \cdot 11}$

Step 1.3.2.1.1.5

Rewrite the expression.

$y = \frac{- 17}{9} \cdot \frac{10 x}{11}$

Step 1.3.2.1.2

Multiply $\frac{- 17}{9}$ by $\frac{10 x}{11}$ .

$y = \frac{- 17 (10 x)}{9 \cdot 11}$

Step 1.3.2.1.3

Simplify the expression.

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Step 1.3.2.1.3.1

Multiply $10$ by $- 17$ .

$y = \frac{- 170 x}{9 \cdot 11}$

Step 1.3.2.1.3.2

Multiply $9$ by $11$ .

$y = \frac{- 170 x}{99}$

Step 1.3.2.1.3.3

Move the negative in front of the fraction.

$y = - \frac{170 x}{99}$

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.

$y = - (\frac{170}{99} x)$

Step 2.2.2

Remove parentheses.

$y = - \frac{170}{99} x$

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 $y = m x + b$ .

$m = - \frac{170}{99}$

$b = 0$

Step 3.2

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

Slope: $- \frac{170}{99}$

y-intercept: $(0, 0)$

Slope: $- \frac{170}{99}$

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.

$y = - (\frac{170}{99} x)$

Step 4.1.2

Remove parentheses.

$y = - \frac{170}{99} x$

Step 4.2

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

$\begin{array}{c} x & y \\ 0 & 0 \\ 99 & - 170 \end{array}$

Step 5

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

Slope: $- \frac{170}{99}$

y-intercept: $(0, 0)$

$\begin{array}{c} x & y \\ 0 & 0 \\ 99 & - 170 \end{array}$

Step 6