# Which of the following equations is parallel to y = (2/3)x + 6 and contains the point (4, -2)?

May 8, 2018

$y = \frac{2}{3} x - \frac{14}{3}$

#### Explanation:

We know that,

$\left(1\right)$ If slop line ${l}_{1}$ is ${m}_{1}$ and slop of ${l}_{2}$ is ${m}_{2}$, then

${l}_{1} / / {l}_{2} \iff {m}_{1} = {m}_{2}$

Here,

${l}_{1} : y = \left(\frac{2}{3}\right) x + 6 , \mathmr{and} {l}_{1} / / {l}_{2}$

Comparing with $y = m x + c$

$\implies$Slop of the line ${l}_{1}$ is ${m}_{1} = \frac{2}{3}$

$\implies$Slop of the line ${l}_{2}$ is ${m}_{2} = \frac{2}{3.} . . \to \left[a s , {m}_{1} = {m}_{2}\right]$

Now, the ' point-slop 'form of line is:

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

For line ${l}_{2}$,$m = \frac{2}{3} \mathmr{and}$point $\left(4 , - 2\right)$

So,the equation of line is:

$y - \left(- 2\right) = \frac{2}{3} \left(x - 4\right)$

$\implies 3 \left(y + 2\right) = 2 \left(x - 4\right)$

$\implies 3 y + 6 = 2 x - 8$

$\implies 3 y = 2 x - 14$

$\implies y = \frac{2}{3} x - \frac{14}{3}$

There is no any equation to compare.!