In a coordinate plane, if the coordinates of two points are (2, 3) and (2, 7), w

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Question: In a coordinate plane, if the coordinates of two points are (2, 3) and (2, 7), what is the slope of the line connecting them?

Options:

Correct Answer: Undefined

Solution:

The slope is calculated as (y2 - y1) / (x2 - x1). Here, (7 - 3) / (2 - 2) is undefined because the denominator is 0.

In a coordinate plane, if the coordinates of two points are (2, 3) and (2, 7), what is the slope of the line connecting them?

In a coordinate plane, if the coordinates of two points are (2, 3) and (2, 7), what is the slope of the line connecting them?

Step 1: Identify the coordinates of the two points. The first point is (2, 3) and the second point is (2, 7).
Step 2: Label the coordinates. Let (x1, y1) = (2, 3) and (x2, y2) = (2, 7).
Step 3: Use the slope formula: slope = (y2 - y1) / (x2 - x1).
Step 4: Substitute the values into the formula: slope = (7 - 3) / (2 - 2).
Step 5: Calculate the difference in y-coordinates: 7 - 3 = 4.
Step 6: Calculate the difference in x-coordinates: 2 - 2 = 0.
Step 7: Now, the slope is 4 / 0.
Step 8: Since you cannot divide by zero, the slope is undefined.

Slope Calculation – The slope of a line is determined by the formula (y2 - y1) / (x2 - x1), which represents the change in y over the change in x.
Vertical Lines – When two points have the same x-coordinate, the line connecting them is vertical, resulting in an undefined slope.