Find the equation of a line which is equidistant from the lines `x = - 7/2 and x = 15/2`

Answer

To find the equation of a line that is equidistant from the lines \( x = -\frac{7}{2} \) and \( x = \frac{15}{2} \), we can follow these steps:

### Step 1: Identify the lines
The two lines given are:
- Line 1: \( x = -\frac{7}{2} \)
- Line 2: \( x = \frac{15}{2} \)

### Step 2: Convert the lines to decimal form
Convert the fractions to decimal for easier calculations:
- \( -\frac{7}{2} = -3.5 \)
- \( \frac{15}{2} = 7.5 \)

### Step 3: Find the midpoint
To find the line that is equidistant from both lines, we need to find the midpoint of the x-coordinates of these two lines. The formula for the midpoint \( M \) between two points \( x_1 \) and \( x_2 \) is:
\[ M = \frac{x_1 + x_2}{2} \]
Here, \( x_1 = -3.5 \) and \( x_2 = 7.5 \).

Substituting the values:
\[ M = \frac{-3.5 + 7.5}{2} \]

### Step 4: Calculate the midpoint
Calculating the sum:
\[ -3.5 + 7.5 = 4 \]
Now, divide by 2:
\[ M = \frac{4}{2} = 2 \]

### Step 5: Write the equation of the line
Since the line we are looking for is vertical (parallel to the y-axis), the equation of the line that is equidistant from both lines is:
\[ x = 2 \]

### Final Answer
The equation of the line which is equidistant from the lines \( x = -\frac{7}{2} \) and \( x = \frac{15}{2} \) is:
\[ \boxed{x = 2} \]

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