# Question 9eed6

Feb 7, 2018

color(green)(C. y - 7 = 2(x - 6)

color(green)(E. y + 1 = 2(x - 2)

#### Explanation:

Let's find the point slope equation for $\left(6 , 7\right)$ and $\left(2 , - 1\right)$

Point slope equations are $m = \frac{y - {y}_{1}}{x - {x}_{1}}$

So let's find the slope first

$m = \frac{y - {y}_{1}}{x - {x}_{1}}$

$m = \frac{7 - \left(- 1\right)}{6 - 2}$

$m = \frac{8}{4} = 2$

Now we have our $m$, let's write our quation

$2 = \frac{y - {y}_{1}}{x - {x}_{1}}$

$\left(y - {y}_{1}\right) = 2 \times \left(x - {x}_{1}\right)$

So let's solve for $\left({x}_{1} , {y}_{1}\right)$ as $\left(6 , 7\right)$:

color(green)(y-7 = 2(x-6)

And also for $\left(2 , - 1\right)$

color(green)(y+1 = 2(x-2)

$\cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot$

$A . y - 1 = 2 \left(x + 2\right)$
$B . y - 7 = \left(x - 6\right)$
$C . y - 7 = 2 \left(x - 6\right)$
$D . y + 1 = \left(x - 2\right)$
$E . y + 1 = 2 \left(x - 2\right)$
$F . y - 7 = \left(x + 6\right)$

First, let's get rid of all the ones that have the wrong $m$:

$A . y - 1 = 2 \left(x + 2\right)$
color(red)(B. y - 7 = (x - 6)
$C . y - 7 = 2 \left(x - 6\right)$
color(red)(D. y + 1 = (x - 2)
$E . y + 1 = 2 \left(x - 2\right)$
color(red)(F.y - 7 = (x + 6)

Now let's see which of the remaining ones look like our answers:

$A . y - 1 = 2 \left(x + 2\right)$
color(green)(C. y - 7 = 2(x - 6)
color(green)(E. y + 1 = 2(x - 2)

Only two. And they are both options, so it looks like color(green)(C# and $\textcolor{g r e e n}{E}$ are the right answers