# What is the equation in point-slope form of the line given (3,7); m=0?

Mar 23, 2018

The line is $y = 7$.

#### Explanation:

The line passes through the points $\left(3 , 7\right)$ and has a slope of $m = 0$.

We know that the slope of a line is given by:

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

And so,

$\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = 0$

$\therefore {x}_{2} \ne {x}_{1} , {y}_{2} = {y}_{1}$

Choosing a y-coordinate, we see that it passes through $\left(3 , 7\right)$, and so ${y}_{2} = {y}_{1} = 7$.

Therefore, the line is $y = 7$.

Here is a graph of the line:

graph{y=0x+7 [-4.54, 18.89, -0.84, 10.875]}