# How do you find the slope of 2x= -8?

Aug 17, 2015

The value of a slope is, strictly speaking, undefined or, in a less rigorous language, infinity.

#### Explanation:

Slope of a straight line in the XY-system of coordinates is defined as a ratio of increment along the Y-axis towards increments of the X-axis.

Let's take two points on a line with coordinates $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$. Then the slope is defined as

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

In case of a line defined by an equation $2 x = - 8$ or, equivalently, $x = - 4$, two points on this line might have different ordinates (Y-coordinates) ${y}_{1}$ and ${y}_{2}$, but must have the same abscissas (X-coordinatex), that is ${x}_{1} = - 4$ and ${x}_{2} = - 4$.

That makes the denominator in the definition of a slope equal to zero and the value of a slope will be undefined.

Using less rigorous language, you may say that the result of division by zero is infinity, and don't bother to ask whether it's positive or negative infinity since it depends on whether ${y}_{1} > {y}_{2}$ or otherwise. I would suggest the strict answer "undefined".