If the slop of line joining the points `(6,-3)` and `(x,7)` is `2`, find the values of `x`.

Answer

To find the value of \( x \) when the slope of the line joining the points \( (6, -3) \) and \( (x, 7) \) is \( 2 \), we can follow these steps:

### Step 1: Use the slope formula
The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
In this case, the points are \( (6, -3) \) and \( (x, 7) \). Here, \( x_1 = 6 \), \( y_1 = -3 \), \( x_2 = x \), and \( y_2 = 7 \).

### Step 2: Substitute the known values into the slope formula
Substituting the values into the slope formula, we get:
\[ 2 = \frac{7 - (-3)}{x - 6} \]

### Step 3: Simplify the equation
Now simplify the numerator:
\[ 7 - (-3) = 7 + 3 = 10 \]
So, the equation becomes:
\[ 2 = \frac{10}{x - 6} \]

### Step 4: Cross-multiply to eliminate the fraction
Cross-multiplying gives:
\[ 2(x - 6) = 10 \]

### Step 5: Distribute and solve for \( x \)
Distributing the \( 2 \):
\[ 2x - 12 = 10 \]
Now, add \( 12 \) to both sides:
\[ 2x = 10 + 12 \]
\[ 2x = 22 \]

### Step 6: Divide by 2 to find \( x \)
Now, divide both sides by \( 2 \):
\[ x = \frac{22}{2} = 11 \]

### Final Answer
Thus, the value of \( x \) is \( 11 \).

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