Finite Math Examples

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

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 $2 x$ from both sides of the equation.

$y = 8 - 2 x$

Step 1.3

Reorder $8$ and $- 2 x$ .

$y = - 2 x + 8$

Step 2

Using the slope-intercept form, the slope is $- 2$ .

$m = - 2$

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 $- 2$ and a given point $(5, 8)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (8) = - 2 \cdot (x - (5))$

Step 5

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

$y - 8 = - 2 \cdot (x - 5)$

Step 6

Solve for $y$ .

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Step 6.1

Simplify $- 2 \cdot (x - 5)$ .

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Step 6.1.1

Rewrite.

$y - 8 = 0 + 0 - 2 \cdot (x - 5)$

Step 6.1.2

Simplify by adding zeros.

$y - 8 = - 2 \cdot (x - 5)$

Step 6.1.3

Apply the distributive property.

$y - 8 = - 2 x - 2 \cdot - 5$

Step 6.1.4

Multiply $- 2$ by $- 5$ .

$y - 8 = - 2 x + 10$

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.

$y = - 2 x + 10 + 8$

Step 6.2.2

Add $10$ and $8$ .

$y = - 2 x + 18$

Step 7