Finite Math Examples

$(- 10, 8)$ , $7 x - 5 y = 2$

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 $7 x$ from both sides of the equation.

$- 5 y = 2 - 7 x$

Step 1.3

Divide each term in $- 5 y = 2 - 7 x$ by $- 5$ and simplify.

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Step 1.3.1

Divide each term in $- 5 y = 2 - 7 x$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{2}{- 5} + \frac{- 7 x}{- 5}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $- 5$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{2}{- 5} + \frac{- 7 x}{- 5}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{2}{- 5} + \frac{- 7 x}{- 5}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Move the negative in front of the fraction.

$y = - \frac{2}{5} + \frac{- 7 x}{- 5}$

Step 1.3.3.1.2

Dividing two negative values results in a positive value.

$y = - \frac{2}{5} + \frac{7 x}{5}$

Step 1.4

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

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Step 1.4.1

Reorder $- \frac{2}{5}$ and $\frac{7 x}{5}$ .

$y = \frac{7 x}{5} - \frac{2}{5}$

Step 1.4.2

Reorder terms.

$y = \frac{7}{5} x - \frac{2}{5}$

Step 2

Using the slope-intercept form, the slope is $\frac{7}{5}$ .

$m = \frac{7}{5}$

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 $\frac{7}{5}$ and a given point $(- 10, 8)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (8) = \frac{7}{5} \cdot (x - (- 10))$

Step 5

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

$y - 8 = \frac{7}{5} \cdot (x + 10)$

Step 6

Solve for $y$ .

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Step 6.1

Simplify $\frac{7}{5} \cdot (x + 10)$ .

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Step 6.1.1

Rewrite.

$y - 8 = 0 + 0 + \frac{7}{5} \cdot (x + 10)$

Step 6.1.2

Simplify by adding zeros.

$y - 8 = \frac{7}{5} \cdot (x + 10)$

Step 6.1.3

Apply the distributive property.

$y - 8 = \frac{7}{5} x + \frac{7}{5} \cdot 10$

Step 6.1.4

Combine $\frac{7}{5}$ and $x$ .

$y - 8 = \frac{7 x}{5} + \frac{7}{5} \cdot 10$

Step 6.1.5

Cancel the common factor of $5$ .

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Step 6.1.5.1

Factor $5$ out of $10$ .

$y - 8 = \frac{7 x}{5} + \frac{7}{5} \cdot (5 (2))$

Step 6.1.5.2

Cancel the common factor.

$y - 8 = \frac{7 x}{5} + \frac{7}{5} \cdot (5 \cdot 2)$

Step 6.1.5.3

Rewrite the expression.

$y - 8 = \frac{7 x}{5} + 7 \cdot 2$

Step 6.1.6

Multiply $7$ by $2$ .

$y - 8 = \frac{7 x}{5} + 14$

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.

$y = \frac{7 x}{5} + 14 + 8$

Step 6.2.2

Add $14$ and $8$ .

$y = \frac{7 x}{5} + 22$

Step 6.3

Reorder terms.

$y = \frac{7}{5} x + 22$

Step 7