7. Given that the slope of any line is defined by slope = rise/run, explain why the calculation of the slope of a vertical line always results in an undefined quantity.

Respuesta :

Slope of a vertical line

We know that a vertical line will always have a null run value

Then run = 0 always

We know that any number divided by 0

Z/0

isn't determinated because if we approximate to 0

Z/1 = Z

Z / 0.1 = 10Z

Z / 0.01 =100 Z

Z / 0.001 = 1000Z

Z / 0.0001 = 10000Z

and so on.

Then if we divide it by a number nearer to zero the answer will be higher and higher, so if Z is divided by zero the result is infinite

If we get approximate to zero by the negative

Z / -1 = -Z

Z / -0.1 = -10Z

Z / -0.01 = -100 Z

Z / -0.001 = -1000Z

Z / -0.0001 = -10000Z

Then if we divide it by a negative number nearer to zero the answer will be lower and lower, so if Z is divided by zero the result is -infinite (negative infinity)

Therefore, if a number is divided by zero it is like if the answer is positive infinity and negative infinity at the same time. So we say it is undefined