# How do you write an equation in point-slope form for the given (6, 1), (-4. 1)?

Aug 23, 2015

$y - 1 = 0 \cdot \left(x - 6\right) \textcolor{w h i t e}{\text{XXXX}}$in explicit point slope form
or$\textcolor{w h i t e}{\text{XXXXX}} y = 1$ in more common form.

#### Explanation:

Given $\left(6 , 1\right)$ and $\left(- 4 , 1\right)$
the change in $y$ is zero
and
since the slope is defined as
$\textcolor{w h i t e}{\text{XXX")m = ("change in y")/("change in x}}$
The slope is
$\textcolor{w h i t e}{\text{XXX}} m = 0$

For a line with slope $m$ through a point $\left(\hat{x} , \hat{y}\right)$
the slope-point form is
$\textcolor{w h i t e}{\text{XXX}} \left(y - \hat{y}\right) = m \left(x - \hat{x}\right)$

We have a slope of $m = 0$ and can use $\left(\hat{x} , \hat{y}\right) = \left(6 , 1\right)$
to obtain the explicit slope-point form shown in the answer.