Question

Jo was finding the slope of the following problem (1,2) and (1,4). When she does the slope formula, she gets 2/0, and she is not sure what this means. Explain to Jo what the slope is and what type of line this slope would give us.

a) The slope represents a vertical line
b) The slope represents a horizontal line
c) The slope represents a diagonal line
d) The slope is undefined

Answer 1

The slope calculated by Jo as 2/0 from points (1,2) and (1,4) represents a vertical line. Since division by zero is not defined in mathematics, the correct choice is (d) The slope is undefined.

Step-by-step explanation:

To explain to Jo what the slope is when she finds it to be 2/0 from the points (1,2) and (1,4): The slope of a line is a measure of its steepness and is calculated by the difference in the y-values (rise) divided by the difference in the x-values (run). Using the slope formula, we subtract the y-values and the x-values of the two points respectively:

• Slope (m) = ∆y / ∆x = (y2 - y1) / (x2 - x1)
• ∆y = 4 - 2 = 2
• ∆x = 1 - 1 = 0

So, the slope m = 2/0. However, division by zero is undefined in mathematics, which means that this slope represents a vertical line. Consequently, the correct answer to the type of line this slope would give us is (d) The slope is undefined.