Pre-Algebra Examples

$\frac{7}{8} y = - 6$

Step 1

Solve for $y$ .

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Step 1.1

Multiply both sides of the equation by $\frac{8}{7}$ .

$\frac{8}{7} \cdot \frac{7 y}{8} = \frac{8}{7} \cdot - 6$

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 $\frac{8}{7} \cdot \frac{7 y}{8}$ .

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Step 1.2.1.1.1

Cancel the common factor of $8$ .

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Step 1.2.1.1.1.1

Cancel the common factor.

$\frac{8}{7} \cdot \frac{7 y}{8} = \frac{8}{7} \cdot - 6$

Step 1.2.1.1.1.2

Rewrite the expression.

$\frac{1}{7} (7 y) = \frac{8}{7} \cdot - 6$

Step 1.2.1.1.2

Cancel the common factor of $7$ .

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Step 1.2.1.1.2.1

Factor $7$ out of $7 y$ .

$\frac{1}{7} (7 (y)) = \frac{8}{7} \cdot - 6$

Step 1.2.1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 y) = \frac{8}{7} \cdot - 6$

Step 1.2.1.1.2.3

Rewrite the expression.

$y = \frac{8}{7} \cdot - 6$

Step 1.2.2

Simplify the right side.

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Step 1.2.2.1

Simplify $\frac{8}{7} \cdot - 6$ .

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Step 1.2.2.1.1

Multiply $\frac{8}{7} \cdot - 6$ .

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Step 1.2.2.1.1.1

Combine $\frac{8}{7}$ and $- 6$ .

$y = \frac{8 \cdot - 6}{7}$

Step 1.2.2.1.1.2

Multiply $8$ by $- 6$ .

$y = \frac{- 48}{7}$

Step 1.2.2.1.2

Move the negative in front of the fraction.

$y = - \frac{48}{7}$

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 $y = m x + b$ .

$m = 0$

$b = - \frac{48}{7}$

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: $(0, - \frac{48}{7})$

Slope: $0$

y-intercept: $(0, - \frac{48}{7})$

Step 3

Find two points on the line.

$\begin{array}{c} x & y \\ 0 & - \frac{48}{7} \\ 1 & - \frac{48}{7} \end{array}$

Step 4

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

Slope: $0$

y-intercept: $(0, - \frac{48}{7})$

$\begin{array}{c} x & y \\ 0 & - \frac{48}{7} \\ 1 & - \frac{48}{7} \end{array}$

Step 5