Question

use the following graphs to answer questions 1 - 4.

1 which of the graphs has a negative slope?
2 which of the graphs has a positive slope?
3 which of the following graphs has an undefined slope?
4 which of the following graphs has a zero slope?

Explanation:

Step1: Recall slope definitions

A negative slope means as \(x\) increases, \(y\) decreases (line goes down from left to right). A positive slope means as \(x\) increases, \(y\) increases (line goes up from left to right). A vertical line has an undefined slope (no change in \(x\)), and a horizontal line has a slope of \(0\) (no change in \(y\)).

Step2: Analyze each graph

• Graph A: Vertical line (undefined slope? Wait, no—wait, the first row: A and B. Wait, the second row: C and D. Let's re-express:
• Graph C: Line going down from left to right (negative slope).
• Graph D: Line going up from left to right (positive slope).
• Graph B: Vertical line (undefined slope, since \(x\) is constant, so \(\frac{\Delta y}{\Delta x}\) is undefined as \(\Delta x = 0\)).
• Graph A: Horizontal line (slope \(0\), since \(\Delta y = 0\), so \(\frac{0}{\Delta x}=0\)).

Step3: Answer each question

1. Negative slope: Graph C (since it decreases left to right).
2. Positive slope: Graph D (increases left to right).
3. Undefined slope: Graph B (vertical line, \(\Delta x = 0\)).
4. Slope of 0: Graph A (horizontal line, \(\Delta y = 0\)).

Answer:

s (for each question):

1. The graph with negative slope is Graph C.
2. The graph with positive slope is Graph D.
3. The graph with an undefined slope is Graph B.
4. The graph with a slope of 0 is Graph A.