# What is the slope for x = 4?

##### 2 Answers

The slope is not defined for points with the same

#### Explanation:

The definition of slope is for the slope of a line through the points

The case

(You may often hear people say that the slope is infinity. This is the result of a confusion of two or more ideas.)

A vertical line has an infinitely steep slope because it's straight up and down!

#### Explanation:

Remember that the a typical equation of a line can be expressed as

where

What this means is that as the top part of the fraction gets big (compared to the denominator), the slope gets steeper and steeper, ever creeping closer to a vertical line. Here you have a slope of just 5:

graph{5x+1 [-11.25, 11.26, -5.63, 5.62]}

And here's a slope of 50:

graph{50x+1 [-11.25, 11.26, -5.63, 5.62]}

So the line becomes vertical as