IF (a,-3) is on the graph of the equation x-4y=14 in the standed (x,y) coordinate plane , then a= ?

Options

A. `-(17)/(4)`
B. `-2`
C. `2`
D. `17`

Answer

To solve the problem, we need to determine the value of \( a \) given that the point \( (a, -3) \) lies on the line defined by the equation \( x - 4y = 14 \).

### Step-by-Step Solution:

1. **Substitute the Coordinates into the Equation:**
We know that the point \( (a, -3) \) means \( x = a \) and \( y = -3 \). We will substitute these values into the equation \( x - 4y = 14 \).

\[ a - 4(-3) = 14 \]

2. **Simplify the Equation:**
Now, simplify the left side of the equation. The term \( -4(-3) \) simplifies to \( +12 \).

\[ a + 12 = 14 \]

3. **Isolate \( a \):**
To find \( a \), we need to isolate it on one side of the equation. We can do this by subtracting \( 12 \) from both sides.

\[ a = 14 - 12 \]

4. **Calculate the Value of \( a \):**
Now, perform the subtraction.

\[ a = 2 \]

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

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