Find the value of c so that the point (3,c) lies on the line represented by 2x-3y+5=0.

Answer

To find the value of \( c \) so that the point \( (3, c) \) lies on the line represented by the equation \( 2x - 3y + 5 = 0 \), we can follow these steps:

### Step 1: Substitute the point into the line equation
We know that the point \( (3, c) \) lies on the line, which means it must satisfy the line's equation. We substitute \( x = 3 \) and \( y = c \) into the equation \( 2x - 3y + 5 = 0 \).

\[ 2(3) - 3(c) + 5 = 0 \]

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

\[ 6 - 3c + 5 = 0 \]

Combine like terms:

\[ 11 - 3c = 0 \]

### Step 3: Solve for \( c \)
To isolate \( c \), we can rearrange the equation:

\[ -3c = -11 \]

Now, divide both sides by -3:

\[ c = \frac{11}{3} \]

### Conclusion
Thus, the value of \( c \) is \( \frac{11}{3} \).

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