Which of the following graphs has a positive , decreasing slope ?

Options

A.
B.
C.
D.

Answer

To determine which graph has a positive but decreasing slope, we can follow these steps:

### Step 1: Understand the Definition of Slope
The slope of a graph at any point is defined as the tangent of the angle (θ) that the tangent line at that point makes with the x-axis. A positive slope means that the angle θ is between 0 and 90 degrees.

**Hint:** Recall that a positive slope indicates that as x increases, y also increases.

### Step 2: Identify the Characteristics of a Decreasing Slope
A decreasing slope means that as you move along the graph, the angle θ decreases. This implies that the value of the slope (tan θ) is also decreasing.

**Hint:** A decreasing slope means that the graph is rising less steeply as you move from left to right.

### Step 3: Analyze Each Graph Option
- **Option 1:** The slope is constant at every point. Since the slope does not change, this cannot be the correct option.

- **Option 2:** The slope changes at different points. As you move along the graph, the angle θ decreases, indicating that the slope is positive but decreasing. This is a potential correct option.

- **Option 3:** The slope is positive but increasing. As you move along the graph, the angle θ increases, which means the slope is not decreasing. This cannot be the correct option.

- **Option 4:** The slope is negative and constant. Since the slope is negative, this cannot be the correct option.

**Hint:** Carefully observe how the slope changes in each graph. Look for the graph where the slope is positive but getting smaller.

### Step 4: Conclusion
After analyzing all the options, we find that **Option 2** is the only graph that has a positive but decreasing slope.

**Final Answer:** The correct option is **Option 2**.