Algebra Examples

$(2, 3)$ , $(7, y)$ $m = - \frac{2}{5}$

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.

$- \frac{2}{5} = \frac{y - (3)}{7 - (2)}$

Step 3

Solve for $y$ .

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Step 3.1

Rewrite the equation as $\frac{y - (3)}{7 - (2)} = - \frac{2}{5}$ .

$\frac{y - (3)}{7 - (2)} = - \frac{2}{5}$

Step 3.2

Multiply both sides of the equation by $7 - (2)$ .

$(7 - 1 \cdot 2) \frac{y - (3)}{7 - 1 \cdot 2} = (7 - (2)) (- \frac{2}{5})$

Step 3.3

Simplify both sides of the equation.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

Simplify $(7 - 1 \cdot 2) \frac{y - (3)}{7 - 1 \cdot 2}$ .

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Step 3.3.1.1.1

Multiply $- 1$ by $3$ .

$(7 - 1 \cdot 2) \frac{y - 3}{7 - 1 \cdot 2} = (7 - (2)) (- \frac{2}{5})$

Step 3.3.1.1.2

Simplify the denominator.

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Step 3.3.1.1.2.1

Multiply $- 1$ by $2$ .

$(7 - 1 \cdot 2) \frac{y - 3}{7 - 2} = (7 - (2)) (- \frac{2}{5})$

Step 3.3.1.1.2.2

Subtract $2$ from $7$ .

$(7 - 1 \cdot 2) \frac{y - 3}{5} = (7 - (2)) (- \frac{2}{5})$

Step 3.3.1.1.3

Reduce the expression by cancelling the common factors.

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Step 3.3.1.1.3.1

Multiply $- 1$ by $2$ .

$(7 - 2) \frac{y - 3}{5} = (7 - (2)) (- \frac{2}{5})$

Step 3.3.1.1.3.2

Subtract $2$ from $7$ .

$5 \frac{y - 3}{5} = (7 - (2)) (- \frac{2}{5})$

Step 3.3.1.1.3.3

Cancel the common factor of $5$ .

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Step 3.3.1.1.3.3.1

Cancel the common factor.

$5 \frac{y - 3}{5} = (7 - (2)) (- \frac{2}{5})$

Step 3.3.1.1.3.3.2

Rewrite the expression.

$y - 3 = (7 - (2)) (- \frac{2}{5})$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Simplify $(7 - (2)) (- \frac{2}{5})$ .

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Step 3.3.2.1.1

Simplify the expression.

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Step 3.3.2.1.1.1

Multiply $- 1$ by $2$ .

$y - 3 = (7 - 2) (- \frac{2}{5})$

Step 3.3.2.1.1.2

Subtract $2$ from $7$ .

$y - 3 = 5 (- \frac{2}{5})$

Step 3.3.2.1.2

Cancel the common factor of $5$ .

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Step 3.3.2.1.2.1

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$y - 3 = 5 (\frac{- 2}{5})$

Step 3.3.2.1.2.2

Cancel the common factor.

$y - 3 = 5 (\frac{- 2}{5})$

Step 3.3.2.1.2.3

Rewrite the expression.

$y - 3 = - 2$

Step 3.4

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

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Step 3.4.1

Add $3$ to both sides of the equation.

$y = - 2 + 3$

Step 3.4.2

Add $- 2$ and $3$ .

$y = 1$