Answer:
Segments with positive slope, negative slope, zero slope and undefined slope are indicated in the attach.
Explanation:
When you represent or consider a segment in a coordinate axis system, the slope of the segment is the variation in "x" axis in relation to variation in "y" axis, it means the quotient Δx/Δy. If we select two different pairs of points (x1, y1) (x2, y2) ⇒slope = Δx/Δy ⇒ slope = (x2 - x1)/(y2 - y1).
There four main options:
- If Δx/Δy > 0 ⇒ Positive slope (In this case: Δx >0 and Δy> 0 or Δx˂ 0 and Δy ˂ 0).
- If Δx/Δy ˂ 0 ⇒Negative slope (this happens when Δx > 0 and Δy˂0 or
Δx˂0 and Δy>0)
- If Δx/Δy = 0 ⇒ zero slope (This happens when Δx =0).
-If Δx/Δy =∅ ⇒ undefined slope (only when Δy = 0).
Given this explanation and considering the word MATH in a coordinated system, we clasiffied the segments as you can see in the attach. Segments denoted by: 1 have positive slopes, 2 negative slopes, 3 zero slope and 4 unddefined slope.