Question

What is the slope of the line that passes through the points ( 5 , 6 )and ( 5 , 9 ) ? Write your answer in simplest form.

Answer 1

The slope of the line that passes through the points (5, 6) and (5, 9) is undefined because the line is vertical, resulting in a 'run' of zero.

Step-by-step explanation:

The slope of a line measures the steepness and direction of the line, calculated as the 'rise' over the 'run,' which means the change in y divided by the change in x. For the given points (5, 6) and (5, 9), we can find the slope by using the formula:

Slope (m) = (y2 - y1) / (x2 - x1)

In this case, the slope is (9 - 6) / (5 - 5), which results in a division by zero. This indicates that the line is a vertical line, which means its slope is undefined. Vertical lines have an undefined slope because their 'run' is zero, and division by zero is not possible in mathematics.

Answer 2

The slope of the line passing through the given points is undefined due to a zero denominator in the slope formula.

Step-by-step explanation:

The slope of a line passing through two points can be found using the formula:
m = (y₂ - y₁)/(x₂ - x₁)
Using the given points (5, 6) and (5, 9), we can plug in the values:
m = (9 - 6)/(5 - 5) = 3/0
However, since the denominator is 0, the slope is undefined.