If the slope of a line passing through the points `(1,4)` and `(x,2)` is `2`, find the value of `x`.

Answer

To find the value of \( x \) given that the slope of the line passing through the points \( (1, 4) \) and \( (x, 2) \) is \( 2 \), we can follow these steps:

### Step 1: Understand the formula for slope
The slope \( m \) of a line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

### Step 2: Assign the points
Let \( (x_1, y_1) = (1, 4) \) and \( (x_2, y_2) = (x, 2) \).

### Step 3: Substitute the points into the slope formula
Using the slope formula, we can write:
\[ 2 = \frac{2 - 4}{x - 1} \]

### Step 4: Simplify the equation
Now simplify the right side:
\[ 2 = \frac{-2}{x - 1} \]

### Step 5: Cross-multiply to eliminate the fraction
Cross-multiplying gives:
\[ 2(x - 1) = -2 \]

### Step 6: Distribute the 2
Distributing the left side results in:
\[ 2x - 2 = -2 \]

### Step 7: Solve for \( x \)
Add \( 2 \) to both sides:
\[ 2x = 0 \]
Now, divide by \( 2 \):
\[ x = 0 \]

### Conclusion
The value of \( x \) is \( 0 \).

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