The slope of the line joining the points `(3,-2)` and `(-1,4)` is ...................

Answer

To find the slope of the line joining the points (3, -2) and (-1, 4), we can use the formula for the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\):

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

### Step 1: Identify the coordinates
Let’s assign the coordinates:
- \( (x_1, y_1) = (3, -2) \)
- \( (x_2, y_2) = (-1, 4) \)

### Step 2: Substitute the values into the slope formula
Now, substituting the values into the slope formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - (-2)}{-1 - 3} \]

### Step 3: Simplify the numerator and denominator
Calculating the numerator:

\[ y_2 - y_1 = 4 - (-2) = 4 + 2 = 6 \]

Calculating the denominator:

\[ x_2 - x_1 = -1 - 3 = -4 \]

### Step 4: Calculate the slope
Now substituting back into the slope formula:

\[ m = \frac{6}{-4} \]

### Step 5: Simplify the slope
Simplifying \(\frac{6}{-4}\):

\[ m = -\frac{3}{2} \]

### Final Answer
Thus, the slope of the line joining the points (3, -2) and (-1, 4) is:

\[ \text{slope} = -\frac{3}{2} \]

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