Finite Math Examples

$4 y - 7 x = - 5$ , $(2, - 2)$

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

Add $7 x$ to both sides of the equation.

$4 y = - 5 + 7 x$

Step 1.3

Divide each term in $4 y = - 5 + 7 x$ by $4$ and simplify.

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Step 1.3.1

Divide each term in $4 y = - 5 + 7 x$ by $4$ .

$\frac{4 y}{4} = \frac{- 5}{4} + \frac{7 x}{4}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $4$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{- 5}{4} + \frac{7 x}{4}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 5}{4} + \frac{7 x}{4}$

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.

$y = - \frac{5}{4} + \frac{7 x}{4}$

Step 1.4

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

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Step 1.4.1

Reorder $- \frac{5}{4}$ and $\frac{7 x}{4}$ .

$y = \frac{7 x}{4} - \frac{5}{4}$

Step 1.4.2

Reorder terms.

$y = \frac{7}{4} x - \frac{5}{4}$

Step 2

Using the slope-intercept form, the slope is $\frac{7}{4}$ .

$m = \frac{7}{4}$

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 $\frac{7}{4}$ and a given point $(2, - 2)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 2) = \frac{7}{4} \cdot (x - (2))$

Step 5

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

$y + 2 = \frac{7}{4} \cdot (x - 2)$

Step 6

Solve for $y$ .

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Step 6.1

Simplify $\frac{7}{4} \cdot (x - 2)$ .

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Step 6.1.1

Rewrite.

$y + 2 = 0 + 0 + \frac{7}{4} \cdot (x - 2)$

Step 6.1.2

Simplify by adding zeros.

$y + 2 = \frac{7}{4} \cdot (x - 2)$

Step 6.1.3

Apply the distributive property.

$y + 2 = \frac{7}{4} x + \frac{7}{4} \cdot - 2$

Step 6.1.4

Combine $\frac{7}{4}$ and $x$ .

$y + 2 = \frac{7 x}{4} + \frac{7}{4} \cdot - 2$

Step 6.1.5

Cancel the common factor of $2$ .

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Step 6.1.5.1

Factor $2$ out of $4$ .

$y + 2 = \frac{7 x}{4} + \frac{7}{2 (2)} \cdot - 2$

Step 6.1.5.2

Factor $2$ out of $- 2$ .

$y + 2 = \frac{7 x}{4} + \frac{7}{2 \cdot 2} \cdot (2 \cdot - 1)$

Step 6.1.5.3

Cancel the common factor.

$y + 2 = \frac{7 x}{4} + \frac{7}{2 \cdot 2} \cdot (2 \cdot - 1)$

Step 6.1.5.4

Rewrite the expression.

$y + 2 = \frac{7 x}{4} + \frac{7}{2} \cdot - 1$

Step 6.1.6

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

$y + 2 = \frac{7 x}{4} + \frac{7 \cdot - 1}{2}$

Step 6.1.7

Simplify the expression.

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Step 6.1.7.1

Multiply $7$ by $- 1$ .

$y + 2 = \frac{7 x}{4} + \frac{- 7}{2}$

Step 6.1.7.2

Move the negative in front of the fraction.

$y + 2 = \frac{7 x}{4} - \frac{7}{2}$

Step 6.2

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

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Step 6.2.1

Subtract $2$ from both sides of the equation.

$y = \frac{7 x}{4} - \frac{7}{2} - 2$

Step 6.2.2

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

$y = \frac{7 x}{4} - \frac{7}{2} - 2 \cdot \frac{2}{2}$

Step 6.2.3

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

$y = \frac{7 x}{4} - \frac{7}{2} + \frac{- 2 \cdot 2}{2}$

Step 6.2.4

Combine the numerators over the common denominator.

$y = \frac{7 x}{4} + \frac{- 7 - 2 \cdot 2}{2}$

Step 6.2.5

Simplify the numerator.

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Step 6.2.5.1

Multiply $- 2$ by $2$ .

$y = \frac{7 x}{4} + \frac{- 7 - 4}{2}$

Step 6.2.5.2

Subtract $4$ from $- 7$ .

$y = \frac{7 x}{4} + \frac{- 11}{2}$

Step 6.2.6

Move the negative in front of the fraction.

$y = \frac{7 x}{4} - \frac{11}{2}$

Step 6.3

Reorder terms.

$y = \frac{7}{4} x - \frac{11}{2}$

Step 7