CA line with a negative slope falls from left to right
DA steeper line always has a larger slope value
A negative slope means y decreases as x increases, so the line falls from left to right — this is correct. A vertical line has undefined slope (division by zero in rise/run), not zero. A horizontal line has slope 0, not undefined. 'Steeper' means larger absolute value: a slope of -5 is steeper than a slope of 1, even though -5 < 1.
Question 2 True / False
If you calculate slope as run/rise instead of rise/run, you get the reciprocal of the correct slope.
TTrue
FFalse
Answer: True
Slope = rise/run. Flipping to run/rise gives the reciprocal. For example, between points with rise 4 and run 2, the correct slope is 4/2 = 2, but run/rise gives 2/4 = 1/2. This reciprocal corresponds to a different (less steep) line — confirming that the order of rise and run matters.
Question 3 Short Answer
Student A computes slope between (2, 5) and (6, 13) as (13 − 5)/(6 − 2) = 2. Student B uses (5 − 13)/(2 − 6) = 2. Why do they get the same answer even though they subtracted in opposite orders?
Think about your answer, then reveal below.
Model answer: Both students subtracted consistently — they both flipped the order of subtraction in both numerator and denominator simultaneously, which is equivalent to multiplying both by -1. The negatives cancel: (-8)/(-4) = 8/4 = 2. Slope is a property of the line, not of which point is labeled first.
The slope formula works with either point as (x₁, y₁) because swapping both subtractions multiplies both rise and run by -1, leaving the ratio unchanged. What causes errors is inconsistency — using (y₂ − y₁) on top but (x₁ − x₂) on the bottom, which flips only one sign and gives the wrong sign for the slope.