Algebra Examples

$(r, 4)$ , $(7, 1)$ , $m = \frac{3}{4}$

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.

$\frac{3}{4} = \frac{1 - (4)}{7 - (r)}$

Step 3

Solve for $r$ .

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Step 3.1

Rewrite the equation as $\frac{1 - (4)}{7 - (r)} = \frac{3}{4}$ .

$\frac{1 - (4)}{7 - (r)} = \frac{3}{4}$

Step 3.2

Simplify both sides.

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Step 3.2.1

Simplify the numerator.

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Step 3.2.1.1

Multiply $- 1$ by $4$ .

$\frac{1 - 4}{7 - r} = \frac{3}{4}$

Step 3.2.1.2

Subtract $4$ from $1$ .

$\frac{- 3}{7 - r} = \frac{3}{4}$

Step 3.2.2

Move the negative in front of the fraction.

$- \frac{3}{7 - r} = \frac{3}{4}$

Step 3.3

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$- 3 \cdot 4 = (7 - r) \cdot 3$

Step 3.4

Solve the equation for $r$ .

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Step 3.4.1

Rewrite the equation as $(7 - r) \cdot 3 = - 3 \cdot 4$ .

$(7 - r) \cdot 3 = - 3 \cdot 4$

Step 3.4.2

Multiply $- 3$ by $4$ .

$(7 - r) \cdot 3 = - 12$

Step 3.4.3

Divide each term in $(7 - r) \cdot 3 = - 12$ by $3$ and simplify.

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Step 3.4.3.1

Divide each term in $(7 - r) \cdot 3 = - 12$ by $3$ .

$\frac{(7 - r) \cdot 3}{3} = \frac{- 12}{3}$

Step 3.4.3.2

Simplify the left side.

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Step 3.4.3.2.1

Cancel the common factor of $3$ .

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Step 3.4.3.2.1.1

Cancel the common factor.

$\frac{(7 - r) \cdot 3}{3} = \frac{- 12}{3}$

Step 3.4.3.2.1.2

Divide $7 - r$ by $1$ .

$7 - r = \frac{- 12}{3}$

Step 3.4.3.3

Simplify the right side.

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Step 3.4.3.3.1

Divide $- 12$ by $3$ .

$7 - r = - 4$

Step 3.4.4

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

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Step 3.4.4.1

Subtract $7$ from both sides of the equation.

$- r = - 4 - 7$

Step 3.4.4.2

Subtract $7$ from $- 4$ .

$- r = - 11$

Step 3.4.5

Divide each term in $- r = - 11$ by $- 1$ and simplify.

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Step 3.4.5.1

Divide each term in $- r = - 11$ by $- 1$ .

$\frac{- r}{- 1} = \frac{- 11}{- 1}$

Step 3.4.5.2

Simplify the left side.

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Step 3.4.5.2.1

Dividing two negative values results in a positive value.

$\frac{r}{1} = \frac{- 11}{- 1}$

Step 3.4.5.2.2

Divide $r$ by $1$ .

$r = \frac{- 11}{- 1}$

Step 3.4.5.3

Simplify the right side.

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Step 3.4.5.3.1

Divide $- 11$ by $- 1$ .

$r = 11$