Which of the following points does not lie on the line `y = 3x + 4` ?

Options

A. (1, 7)
B. (2, 10)
C. `(-1, 1)`
D. (4, 12)

Explanation

To determine which of the given points does not lie on the line represented by the equation \( y = 3x + 4 \), we will substitute the x-coordinates of each point into the equation and check if the corresponding y-coordinate matches.

### Given Points:
1. (1, 7)
2. (2, 10)
3. (-1, 1)
4. (4, 12)

### Step-by-Step Solution:

**Step 1: Check the first point (1, 7)**
Substitute \( x = 1 \) into the equation \( y = 3x + 4 \):
\[ y = 3(1) + 4 = 3 + 4 = 7 \]
Since the calculated \( y \) value (7) matches the given \( y \) value (7), the point (1, 7) lies on the line.

**Step 2: Check the second point (2, 10)**
Substitute \( x = 2 \) into the equation \( y = 3x + 4 \):
\[ y = 3(2) + 4 = 6 + 4 = 10 \]
Since the calculated \( y \) value (10) matches the given \( y \) value (10), the point (2, 10) lies on the line.

**Step 3: Check the third point (-1, 1)**
Substitute \( x = -1 \) into the equation \( y = 3x + 4 \):
\[ y = 3(-1) + 4 = -3 + 4 = 1 \]
Since the calculated \( y \) value (1) matches the given \( y \) value (1), the point (-1, 1) lies on the line.

**Step 4: Check the fourth point (4, 12)**
Substitute \( x = 4 \) into the equation \( y = 3x + 4 \):
\[ y = 3(4) + 4 = 12 + 4 = 16 \]
Since the calculated \( y \) value (16) does not match the given \( y \) value (12), the point (4, 12) does not lie on the line.

### Conclusion:
The point that does not lie on the line \( y = 3x + 4 \) is **(4, 12)**.

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