Line L passes through the coordinate points `((-7)/(2), 3) and ((-3)/(2), 5)`. What is the slope of line L?

Options

A. `-1`
B. `(-2)/(5)`
C. `(2)/(5)`
D. `1`

Explanation

To find the slope of line L that passes through the points \((-7/2, 3)\) and \((-3/2, 5)\), we can use the formula for the slope \(m\):

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

### Step 1: Identify the coordinates
Let’s assign the coordinates:
- Point 1: \((x_1, y_1) = \left(-\frac{7}{2}, 3\right)\)
- Point 2: \((x_2, y_2) = \left(-\frac{3}{2}, 5\right)\)

### Step 2: Substitute the values into the slope formula
Now we substitute the values into the slope formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 3}{-\frac{3}{2} - \left(-\frac{7}{2}\right)} \]

### Step 3: Simplify the numerator
Calculate the numerator:

\[ 5 - 3 = 2 \]

### Step 4: Simplify the denominator
Now calculate the denominator:

\[ -\frac{3}{2} - \left(-\frac{7}{2}\right) = -\frac{3}{2} + \frac{7}{2} = \frac{7 - 3}{2} = \frac{4}{2} = 2 \]

### Step 5: Calculate the slope
Now substitute back into the slope formula:

\[ m = \frac{2}{2} = 1 \]

### Final Answer
The slope of line L is \(m = 1\).

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