Algebra Examples

$(3, - 5)$ and $(5, - 1)$

Step 1

Find the slope of the line between $(3, - 5)$ and $(5, - 1)$ using $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , which is the change of $y$ over the change of $x$ .

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Step 1.1

Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

$m = \frac{change in y}{change in x}$

Step 1.2

The change in $x$ is equal to the difference in x-coordinates (also called run), and the change in $y$ is equal to the difference in y-coordinates (also called rise).

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

Step 1.3

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{- 1 - (- 5)}{5 - (3)}$

Step 1.4

Simplify.

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Step 1.4.1

Simplify the numerator.

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Step 1.4.1.1

Multiply $- 1$ by $- 5$ .

$m = \frac{- 1 + 5}{5 - (3)}$

Step 1.4.1.2

Add $- 1$ and $5$ .

$m = \frac{4}{5 - (3)}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 1$ by $3$ .

$m = \frac{4}{5 - 3}$

Step 1.4.2.2

Subtract $3$ from $5$ .

$m = \frac{4}{2}$

Step 1.4.3

Divide $4$ by $2$ .

$m = 2$

Step 2

Use the slope $2$ and a given point $(3, - 5)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 5) = 2 \cdot (x - (3))$

Step 3

Simplify the equation and keep it in point-slope form.

$y + 5 = 2 \cdot (x - 3)$

Step 4

Solve for $y$ .

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Step 4.1

Simplify $2 \cdot (x - 3)$ .

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Step 4.1.1

Rewrite.

$y + 5 = 0 + 0 + 2 \cdot (x - 3)$

Step 4.1.2

Simplify by adding zeros.

$y + 5 = 2 \cdot (x - 3)$

Step 4.1.3

Apply the distributive property.

$y + 5 = 2 x + 2 \cdot - 3$

Step 4.1.4

Multiply $2$ by $- 3$ .

$y + 5 = 2 x - 6$

Step 4.2

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

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Step 4.2.1

Subtract $5$ from both sides of the equation.

$y = 2 x - 6 - 5$

Step 4.2.2

Subtract $5$ from $- 6$ .

$y = 2 x - 11$

Step 5