Final answer:
The correct answer is option C. The point is above the line. The point (4, 1) is not a solution to the equation y = 3x + 1 because the y-value of the point does not satisfy the equation.
Step-by-step explanation:
To determine if a point is a solution to an equation, we substitute the x and y values of the point into the equation and check if the equation holds true. Let's do this for the point (4, 1) and the equation y = 3x + 1:
Substituting x = 4 and y = 1 into the equation, we get:
y = 3(4) + 1
y = 12 + 1
y = 13
The y-value of the point (4, 1) is 13, which is not equal to the calculated value of y = 13. Therefore, the point (4, 1) is not a solution to the equation y = 3x + 1.
The point (4, 1) is not a solution to the equation y = 3x + 1 because when we plug in the value of x = 4 into the equation, we expect the value of y to be 3(4) + 1 = 13, not 1. Since 1 is not equal to 13, the point (4, 1) does not satisfy the equation. Instead, this point lies below the line represented by the equation.
To further clarify, for a point to be on a line, the x and y coordinates must satisfy the line's equation. For the equation y = 3x + 1, any point that is a solution will have a y-coordinate that is three times its x-coordinate plus 1. Since this is not true for the point (4, 1), we can conclude that it is not on the line. Therefore, option D, indicating that the point is below the line, is the correct choice.