Finite Math Examples

$(7, 8)$ , $x + 2 y = 5$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 1.2

Subtract $x$ from both sides of the equation.

$2 y = 5 - x$

Step 1.3

Divide each term in $2 y = 5 - x$ by $2$ and simplify.

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Step 1.3.1

Divide each term in $2 y = 5 - x$ by $2$ .

$\frac{2 y}{2} = \frac{5}{2} + \frac{- x}{2}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $2$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{5}{2} + \frac{- x}{2}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{5}{2} + \frac{- x}{2}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Move the negative in front of the fraction.

$y = \frac{5}{2} - \frac{x}{2}$

Step 1.4

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

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Step 1.4.1

Reorder $\frac{5}{2}$ and $- \frac{x}{2}$ .

$y = - \frac{x}{2} + \frac{5}{2}$

Step 1.4.2

Reorder terms.

$y = - (\frac{1}{2} x) + \frac{5}{2}$

Step 1.4.3

Remove parentheses.

$y = - \frac{1}{2} x + \frac{5}{2}$

Step 2

Using the slope-intercept form, the slope is $- \frac{1}{2}$ .

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

Step 3

To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.

Step 4

Use the slope $- \frac{1}{2}$ and a given point $(7, 8)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (8) = - \frac{1}{2} \cdot (x - (7))$

Step 5

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

$y - 8 = - \frac{1}{2} \cdot (x - 7)$

Step 6

Solve for $y$ .

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Step 6.1

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

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Step 6.1.1

Rewrite.

$y - 8 = 0 + 0 - \frac{1}{2} \cdot (x - 7)$

Step 6.1.2

Simplify by adding zeros.

$y - 8 = - \frac{1}{2} \cdot (x - 7)$

Step 6.1.3

Apply the distributive property.

$y - 8 = - \frac{1}{2} x - \frac{1}{2} \cdot - 7$

Step 6.1.4

Combine $x$ and $\frac{1}{2}$ .

$y - 8 = - \frac{x}{2} - \frac{1}{2} \cdot - 7$

Step 6.1.5

Multiply $- \frac{1}{2} \cdot - 7$ .

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Step 6.1.5.1

Multiply $- 7$ by $- 1$ .

$y - 8 = - \frac{x}{2} + 7 (\frac{1}{2})$

Step 6.1.5.2

Combine $7$ and $\frac{1}{2}$ .

$y - 8 = - \frac{x}{2} + \frac{7}{2}$

Step 6.2

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

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Step 6.2.1

Add $8$ to both sides of the equation.

$y = - \frac{x}{2} + \frac{7}{2} + 8$

Step 6.2.2

To write $8$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = - \frac{x}{2} + \frac{7}{2} + 8 \cdot \frac{2}{2}$

Step 6.2.3

Combine $8$ and $\frac{2}{2}$ .

$y = - \frac{x}{2} + \frac{7}{2} + \frac{8 \cdot 2}{2}$

Step 6.2.4

Combine the numerators over the common denominator.

$y = - \frac{x}{2} + \frac{7 + 8 \cdot 2}{2}$

Step 6.2.5

Simplify the numerator.

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Step 6.2.5.1

Multiply $8$ by $2$ .

$y = - \frac{x}{2} + \frac{7 + 16}{2}$

Step 6.2.5.2

Add $7$ and $16$ .

$y = - \frac{x}{2} + \frac{23}{2}$

Step 6.3

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

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Step 6.3.1

Reorder terms.

$y = - (\frac{1}{2} x) + \frac{23}{2}$

Step 6.3.2

Remove parentheses.

$y = - \frac{1}{2} x + \frac{23}{2}$

Step 7