Algebra Examples

$(- 3, - 2)$ and $(x, 6)$ , $m = 2$

Step 1

Slope $m$ is equal to the change in $y$ over the change in $x$ .

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Step 2

Substitute in the values of the known parameters.

$2 = \frac{6 - (- 2)}{x - (- 3)}$

Step 3

Solve for $x$ .

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Step 3.1

Rewrite the equation as $\frac{6 - (- 2)}{x - (- 3)} = 2$ .

$\frac{6 - (- 2)}{x - (- 3)} = 2$

Step 3.2

Factor each term.

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Step 3.2.1

Multiply $- 1$ by $- 2$ .

$\frac{6 + 2}{x - (- 3)} = 2$

Step 3.2.2

Add $6$ and $2$ .

$\frac{8}{x - (- 3)} = 2$

Step 3.2.3

Multiply $- 1$ by $- 3$ .

$\frac{8}{x + 3} = 2$

Step 3.3

Find the LCD of the terms in the equation.

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Step 3.3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x + 3, 1$

Step 3.3.2

Remove parentheses.

$x + 3, 1$

Step 3.3.3

The LCM of one and any expression is the expression.

$x + 3$

Step 3.4

Multiply each term in $\frac{8}{x + 3} = 2$ by $x + 3$ to eliminate the fractions.

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Step 3.4.1

Multiply each term in $\frac{8}{x + 3} = 2$ by $x + 3$ .

$\frac{8}{x + 3} (x + 3) = 2 (x + 3)$

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $x + 3$ .

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Step 3.4.2.1.1

Cancel the common factor.

$\frac{8}{x + 3} (x + 3) = 2 (x + 3)$

Step 3.4.2.1.2

Rewrite the expression.

$8 = 2 (x + 3)$

Step 3.4.3

Simplify the right side.

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Step 3.4.3.1

Apply the distributive property.

$8 = 2 x + 2 \cdot 3$

Step 3.4.3.2

Multiply $2$ by $3$ .

$8 = 2 x + 6$

Step 3.5

Solve the equation.

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Step 3.5.1

Rewrite the equation as $2 x + 6 = 8$ .

$2 x + 6 = 8$

Step 3.5.2

Move all terms not containing $x$ to the right side of the equation.

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Step 3.5.2.1

Subtract $6$ from both sides of the equation.

$2 x = 8 - 6$

Step 3.5.2.2

Subtract $6$ from $8$ .

$2 x = 2$

Step 3.5.3

Divide each term in $2 x = 2$ by $2$ and simplify.

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Step 3.5.3.1

Divide each term in $2 x = 2$ by $2$ .

$\frac{2 x}{2} = \frac{2}{2}$

Step 3.5.3.2

Simplify the left side.

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Step 3.5.3.2.1

Cancel the common factor of $2$ .

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Step 3.5.3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{2}{2}$

Step 3.5.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{2}{2}$

Step 3.5.3.3

Simplify the right side.

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Step 3.5.3.3.1

Divide $2$ by $2$ .

$x = 1$