Finite Math Examples

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

Step 1

The standard form of a linear equation is $A x + B y = C$ .

Step 2

Multiply both sides by $7$ .

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

Step 3

Simplify the left side.

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Step 3.1

Simplify $7 (y + 1)$ .

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Step 3.1.1

Apply the distributive property.

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

Step 3.1.2

Multiply $7$ by $1$ .

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

Step 4

Simplify the right side.

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Step 4.1

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

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Step 4.1.1

Apply the distributive property.

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

Step 4.1.2

Combine $\frac{8}{7}$ and $x$ .

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

Step 4.1.3

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

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Step 4.1.3.1

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

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

Step 4.1.3.2

Multiply $8$ by $- 6$ .

$7 y + 7 = 7 (\frac{8 x}{7} + \frac{- 48}{7})$

Step 4.1.4

Move the negative in front of the fraction.

$7 y + 7 = 7 (\frac{8 x}{7} - \frac{48}{7})$

Step 4.1.5

Apply the distributive property.

$7 y + 7 = 7 \frac{8 x}{7} + 7 (- \frac{48}{7})$

Step 4.1.6

Cancel the common factor of $7$ .

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Step 4.1.6.1

Cancel the common factor.

$7 y + 7 = 7 \frac{8 x}{7} + 7 (- \frac{48}{7})$

Step 4.1.6.2

Rewrite the expression.

$7 y + 7 = 8 x + 7 (- \frac{48}{7})$

Step 4.1.7

Cancel the common factor of $7$ .

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Step 4.1.7.1

Move the leading negative in $- \frac{48}{7}$ into the numerator.

$7 y + 7 = 8 x + 7 (\frac{- 48}{7})$

Step 4.1.7.2

Cancel the common factor.

$7 y + 7 = 8 x + 7 (\frac{- 48}{7})$

Step 4.1.7.3

Rewrite the expression.

$7 y + 7 = 8 x - 48$

Step 5

Rewrite the equation.

$8 x - 48 = 7 y + 7$

Step 6

Move all terms containing variables to the left side of the equation.

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Step 6.1

Subtract $7 y$ from both sides of the equation.

$8 x - 48 - 7 y = 7$

Step 6.2

Move $- 48$ .

$8 x - 7 y - 48 = 7$

Step 7

Move all terms not containing a variable to the right side of the equation.

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Step 7.1

Add $48$ to both sides of the equation.

$8 x - 7 y = 7 + 48$

Step 7.2

Add $7$ and $48$ .

$8 x - 7 y = 55$

Step 8