Algebra Examples

$(5, 0)$ and $(- 3, 6)$

Step 1

Find the slope of the line between $(5, 0)$ and $(- 3, 6)$ 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.

$m = \frac{6 - (0)}{- 3 - (5)}$

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 $0$ .

$m = \frac{6 + 0}{- 3 - (5)}$

Step 1.4.1.2

Add $6$ and $0$ .

$m = \frac{6}{- 3 - (5)}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 1$ by $5$ .

$m = \frac{6}{- 3 - 5}$

Step 1.4.2.2

Subtract $5$ from $- 3$ .

$m = \frac{6}{- 8}$

Step 1.4.3

Reduce the expression by cancelling the common factors.

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Step 1.4.3.1

Cancel the common factor of $6$ and $- 8$ .

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Step 1.4.3.1.1

Factor $2$ out of $6$ .

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

Step 1.4.3.1.2

Cancel the common factors.

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Step 1.4.3.1.2.1

Factor $2$ out of $- 8$ .

$m = \frac{2 \cdot 3}{2 \cdot - 4}$

Step 1.4.3.1.2.2

Cancel the common factor.

$m = \frac{2 \cdot 3}{2 \cdot - 4}$

Step 1.4.3.1.2.3

Rewrite the expression.

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

Step 1.4.3.2

Move the negative in front of the fraction.

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

Step 2

Use the slope $- \frac{3}{4}$ and a given point $(5, 0)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = - \frac{3}{4} \cdot (x - (5))$

Step 3

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

$y + 0 = - \frac{3}{4} \cdot (x - 5)$

Step 4

Write the equation in $y = m x + b$ form.

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Step 4.1

Solve for $y$ .

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Step 4.1.1

Add $y$ and $0$ .

$y = - \frac{3}{4} \cdot (x - 5)$

Step 4.1.2

Simplify $- \frac{3}{4} \cdot (x - 5)$ .

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Step 4.1.2.1

Apply the distributive property.

$y = - \frac{3}{4} x - \frac{3}{4} \cdot - 5$

Step 4.1.2.2

Combine $x$ and $\frac{3}{4}$ .

$y = - \frac{x \cdot 3}{4} - \frac{3}{4} \cdot - 5$

Step 4.1.2.3

Multiply $- \frac{3}{4} \cdot - 5$ .

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Step 4.1.2.3.1

Multiply $- 5$ by $- 1$ .

$y = - \frac{x \cdot 3}{4} + 5 (\frac{3}{4})$

Step 4.1.2.3.2

Combine $5$ and $\frac{3}{4}$ .

$y = - \frac{x \cdot 3}{4} + \frac{5 \cdot 3}{4}$

Step 4.1.2.3.3

Multiply $5$ by $3$ .

$y = - \frac{x \cdot 3}{4} + \frac{15}{4}$

Step 4.1.2.4

Move $3$ to the left of $x$ .

$y = - \frac{3 x}{4} + \frac{15}{4}$

Step 4.2

Reorder terms.

$y = - (\frac{3}{4} x) + \frac{15}{4}$

Step 4.3

Remove parentheses.

$y = - \frac{3}{4} x + \frac{15}{4}$

Step 5