# How do you write an equation in point-slope form for the given (-1, 7), (5, 7)?

Jul 22, 2015

Calculate the slope between the two given points and using that slope and either of the points write in point slope form as;
$\textcolor{w h i t e}{\text{XXXX}}$ y-7 = 0(x-5)

#### Explanation:

Step 1: Determine the slope
Slope of a line between two points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ is
$\textcolor{w h i t e}{\text{XXXX}}$$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

For the given points $\left(- 1 , 7\right)$ and $\left(5 , 7\right)$, this becomes
$\textcolor{w h i t e}{\text{XXXX}}$$m = \frac{7 - 7}{5 - \left(- 1\right)} = 0$

Step 2: Write in slope point form
For a slope of $m$ and a point$\left(\hat{x} , \hat{y}\right)$
the point-slope form is
$\textcolor{w h i t e}{\text{XXXX}}$$y - \hat{y} = m \left(x - \hat{x}\right)$

If we choose to use $\left(\hat{x} , \hat{y}\right) = \left(5 , 7\right)$
and our previously determined value for $m$
this becomes:
$\textcolor{w h i t e}{\text{XXXX}}$$y - 7 = 0 \left(x - 5\right)$

Note that this is an unusual form, but it is this the formal "point-slope version.