Finite Math Examples

$(4, - 9)$ , $y = \frac{9}{4} - \frac{7}{4}$

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

Simplify the right side.

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Step 1.2.1

Simplify $\frac{9}{4} - \frac{7}{4}$ .

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Step 1.2.1.1

Combine the numerators over the common denominator.

$y = \frac{9 - 7}{4}$

Step 1.2.1.2

Subtract $7$ from $9$ .

$y = \frac{2}{4}$

Step 1.2.1.3

Cancel the common factor of $2$ and $4$ .

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Step 1.2.1.3.1

Factor $2$ out of $2$ .

$y = \frac{2 (1)}{4}$

Step 1.2.1.3.2

Cancel the common factors.

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Step 1.2.1.3.2.1

Factor $2$ out of $4$ .

$y = \frac{2 \cdot 1}{2 \cdot 2}$

Step 1.2.1.3.2.2

Cancel the common factor.

$y = \frac{2 \cdot 1}{2 \cdot 2}$

Step 1.2.1.3.2.3

Rewrite the expression.

$y = \frac{1}{2}$

Step 2

Using the slope-intercept form, the slope is $0$ .

$m = 0$

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 $0$ and a given point $(4, - 9)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 9) = 0 \cdot (x - (4))$

Step 5

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

$y + 9 = 0 \cdot (x - 4)$

Step 6

Solve for $y$ .

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Step 6.1

Multiply $0$ by $x - 4$ .

$y + 9 = 0$

Step 6.2

Subtract $9$ from both sides of the equation.

$y = - 9$

Step 7