Example of undefined slope
An example of undefined slope occurs when the line is vertical
An example of undefined slope occurs when the line is vertical. In other words, when a line is perfectly perpendicular to the x-axis, the slope of that line is undefined. This is because division by zero is undefined, and the slope of a line is determined by dividing the change in y-coordinates by the change in x-coordinates.
For instance, consider the equation of a vertical line x = 3. This means that for every y-coordinate, the x-coordinate is constant at 3. If we choose any two points on this line, let’s say (3, 1) and (3, 5), the change in x-coordinates is 0, since both x-values are the same. The change in y-coordinates is 5 – 1 = 4. Therefore, the slope of this vertical line would be 4/0, which is undefined.
Visually, a line with an undefined slope appears as a vertical line that extends infinitely up and down or has a steep incline that approaches infinity.
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