If the point (5,2) lies on the graph of the linear eqaution kx +5y =10 k find k

Answer

To find the value of \( k \) in the equation \( kx + 5y = 10k \) given that the point \( (5, 2) \) lies on its graph, we can follow these steps:

### Step 1: Substitute the coordinates into the equation
We know the point \( (5, 2) \) means \( x = 5 \) and \( y = 2 \). We will substitute these values into the equation \( kx + 5y = 10k \).

\[ k(5) + 5(2) = 10k \]

### Step 2: Simplify the equation
Now, we simplify the left-hand side:

\[ 5k + 10 = 10k \]

### Step 3: Rearrange the equation
Next, we will rearrange the equation to isolate \( k \). We can move \( 5k \) to the right side:

\[ 10 = 10k - 5k \]

This simplifies to:

\[ 10 = 5k \]

### Step 4: Solve for \( k \)
Now, we divide both sides by 5 to find \( k \):

\[ k = \frac{10}{5} \]

This gives us:

\[ k = 2 \]

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

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