If the slope of the line joining the points (k,-3) and (-6,-8) is `5/4` ,then the value of k is

Options

A. 2
B. -2
C. 3
D. -3

Answer

To find the value of \( k \) given that the slope of the line joining the points \( (k, -3) \) and \( (-6, -8) \) is \( \frac{5}{4} \), we can follow these steps:

### Step 1: Write the formula for the slope
The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

### Step 2: Identify the points
Here, we have:
- Point 1: \( (k, -3) \) which gives \( x_1 = k \) and \( y_1 = -3 \)
- Point 2: \( (-6, -8) \) which gives \( x_2 = -6 \) and \( y_2 = -8 \)

### Step 3: Substitute the values into the slope formula
Substituting the values into the slope formula, we get:
\[ \frac{5}{4} = \frac{-8 - (-3)}{-6 - k} \]

### Step 4: Simplify the equation
This simplifies to:
\[ \frac{5}{4} = \frac{-8 + 3}{-6 - k} \]
\[ \frac{5}{4} = \frac{-5}{-6 - k} \]

### Step 5: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 5(-6 - k) = 4(-5) \]

### Step 6: Distribute and simplify
Distributing both sides:
\[ -30 - 5k = -20 \]

### Step 7: Solve for \( k \)
Now, we can isolate \( k \):
\[ -5k = -20 + 30 \]
\[ -5k = 10 \]
\[ k = \frac{10}{-5} \]
\[ k = -2 \]

### Final Answer
Thus, the value of \( k \) is \( -2 \).

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