Pre-Algebra Examples

$- \frac{3}{7} y = 9$

Step 1

Solve for $y$ .

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Step 1.1

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

$- \frac{7}{3} (- \frac{3 y}{7}) = - \frac{7}{3} \cdot 9$

Step 1.2

Simplify both sides of the equation.

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Step 1.2.1

Simplify the left side.

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Step 1.2.1.1

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

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Step 1.2.1.1.1

Cancel the common factor of $7$ .

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Step 1.2.1.1.1.1

Move the leading negative in $- \frac{7}{3}$ into the numerator.

$\frac{- 7}{3} (- \frac{3 y}{7}) = - \frac{7}{3} \cdot 9$

Step 1.2.1.1.1.2

Move the leading negative in $- \frac{3 y}{7}$ into the numerator.

$\frac{- 7}{3} \cdot \frac{- 3 y}{7} = - \frac{7}{3} \cdot 9$

Step 1.2.1.1.1.3

Factor $7$ out of $- 7$ .

$\frac{7 (- 1)}{3} \cdot \frac{- 3 y}{7} = - \frac{7}{3} \cdot 9$

Step 1.2.1.1.1.4

Cancel the common factor.

$\frac{7 \cdot - 1}{3} \cdot \frac{- 3 y}{7} = - \frac{7}{3} \cdot 9$

Step 1.2.1.1.1.5

Rewrite the expression.

$\frac{- 1}{3} (- 3 y) = - \frac{7}{3} \cdot 9$

Step 1.2.1.1.2

Cancel the common factor of $3$ .

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Step 1.2.1.1.2.1

Factor $3$ out of $- 3 y$ .

$\frac{- 1}{3} (3 (- y)) = - \frac{7}{3} \cdot 9$

Step 1.2.1.1.2.2

Cancel the common factor.

$\frac{- 1}{3} (3 (- y)) = - \frac{7}{3} \cdot 9$

Step 1.2.1.1.2.3

Rewrite the expression.

$- - y = - \frac{7}{3} \cdot 9$

Step 1.2.1.1.3

Multiply.

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Step 1.2.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{7}{3} \cdot 9$

Step 1.2.1.1.3.2

Multiply $y$ by $1$ .

$y = - \frac{7}{3} \cdot 9$

Step 1.2.2

Simplify the right side.

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Step 1.2.2.1

Simplify $- \frac{7}{3} \cdot 9$ .

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Step 1.2.2.1.1

Cancel the common factor of $3$ .

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Step 1.2.2.1.1.1

Move the leading negative in $- \frac{7}{3}$ into the numerator.

$y = \frac{- 7}{3} \cdot 9$

Step 1.2.2.1.1.2

Factor $3$ out of $9$ .

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

Step 1.2.2.1.1.3

Cancel the common factor.

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

Step 1.2.2.1.1.4

Rewrite the expression.

$y = - 7 \cdot 3$

Step 1.2.2.1.2

Multiply $- 7$ by $3$ .

$y = - 21$

Step 2

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

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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

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

$m = 0$

$b = - 21$

Step 2.3

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

Slope: $0$

y-intercept: $(0, - 21)$

Slope: $0$

y-intercept: $(0, - 21)$

Step 3

Find two points on the line.

$\begin{array}{c} x & y \\ 0 & - 21 \\ 1 & - 21 \end{array}$

Step 4

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

Slope: $0$

y-intercept: $(0, - 21)$

$\begin{array}{c} x & y \\ 0 & - 21 \\ 1 & - 21 \end{array}$

Step 5