The points `(3,4)` and `(2,-6)` are situated on the .......... Of the line `3x-4y-8-=0`

Explanation

To determine the position of the points \( (3, 4) \) and \( (2, -6) \) relative to the line defined by the equation \( 3x - 4y - 8 = 0 \), we can follow these steps:

### Step 1: Substitute the coordinates of the first point \( (3, 4) \) into the line equation.
We start by substituting \( x = 3 \) and \( y = 4 \) into the equation \( 3x - 4y - 8 = 0 \).

\[ 3(3) - 4(4) - 8 = 0 \]

Calculating this gives:

\[ 9 - 16 - 8 = -15 \]

### Step 2: Determine the sign of the result for point \( (3, 4) \).
The result from Step 1 is \( -15 \), which is less than \( 0 \). This indicates that the point \( (3, 4) \) lies on one side of the line.

### Step 3: Substitute the coordinates of the second point \( (2, -6) \) into the line equation.
Next, we substitute \( x = 2 \) and \( y = -6 \) into the equation \( 3x - 4y - 8 = 0 \).

\[ 3(2) - 4(-6) - 8 = 0 \]

Calculating this gives:

\[ 6 + 24 - 8 = 22 \]

### Step 4: Determine the sign of the result for point \( (2, -6) \).
The result from Step 3 is \( 22 \), which is greater than \( 0 \). This indicates that the point \( (2, -6) \) lies on the opposite side of the line compared to point \( (3, 4) \).

### Conclusion
Since point \( (3, 4) \) gives a negative result and point \( (2, -6) \) gives a positive result when substituted into the line equation, we conclude that the points \( (3, 4) \) and \( (2, -6) \) are situated on opposite sides of the line \( 3x - 4y - 8 = 0 \).

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