# What is the equation of the line with slope  m= -36/49  that passes through  (-6/7, 16/21) ?

May 4, 2017

$y = - \frac{36}{49} x + \frac{1432}{1029}$ or

$y = - \frac{36}{49} x + 1 \frac{403}{1029}$

#### Explanation:

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

From the question, we get the following information:

$m = - \frac{36}{49} ,$

${x}_{1} , {y}_{1} = \left(- \frac{6}{7} , \frac{16}{21}\right)$

The point slope equation.

$y - \frac{16}{21} = - \frac{36}{49} \left(x - \frac{6}{7}\right)$

Simplify.

$y - \frac{16}{21} = - \frac{36}{49} x + \frac{216}{343}$$\Leftarrow$ Multiplying two negatives gives a positive result.

Add $\frac{16}{21}$ to both sides.

$y - \textcolor{red}{\cancel{\textcolor{b l a c k}{\frac{16}{21}}}} + \textcolor{red}{\cancel{\textcolor{b l a c k}{\frac{16}{21}}}} = - \frac{36}{49} x + \frac{216}{343} + \frac{16}{21}$

Simplify.

$y = - \frac{36}{49} x + \frac{216}{343} + \frac{16}{21}$

When adding fractions, the denominators must be the same. The Least Common Denominator (LCD) can be found by factoring the denominators.

Prime factorize the denominators $343$ and $21$.

$343 :$$7 \times 7 \times 7$

$21 :$$3 \times 7$

$\text{LCD} = 3 \times 7 \times 7 \times 7 = 1029$

Multiply each fraction by the equivalent fraction that will result in the LCD $1029$. An equivalent fraction is equal to $1$, such as $\frac{2}{2} = 1$.

$y = - \frac{36}{49} x - \frac{216}{343} \times \textcolor{red}{\frac{3}{3}} + \frac{16}{21} \times \textcolor{g r e e n}{\frac{49}{49}}$

Simplify.

$y = - \frac{36}{49} x + \frac{648}{1029} + \frac{784}{1029}$

Simplify.

$y = - \frac{36}{49} x + \frac{1432}{1029}$ or

$y = - \frac{36}{49} x + 1 \frac{403}{1029}$

May 4, 2017

$y = - \frac{36}{49} x + \frac{136}{1029}$

#### Explanation:

Use the slope - intercept equation:$y = m x + b$

$y = - \frac{36}{49} x + b$

Put the point $\left(- \frac{6}{7} , \frac{16}{21}\right)$ into the equation as $x \text{ and } y$:

$\frac{16}{21} = - \frac{36}{49} \cdot - \frac{6}{7} + b$

$\frac{16}{21} = \frac{216}{343} + b$

$b = \frac{16}{21} - \frac{216}{343}$

Find a common denominator: 21 = 3 * 7; 343 = 7^3#

Common denominator $= 3 \cdot {7}^{3} = 1029$

$b = \frac{16}{21} \cdot \frac{49}{49} - \frac{216}{343} \cdot \frac{3}{3} = \frac{784}{1029} - \frac{648}{1029} = \frac{136}{1029}$

$y = - \frac{36}{49} x + \frac{136}{1029}$