Final answer:
The student switched the x and y values, which is incorrect. By substituting x=4 into the equation y = 3x + 1, we find y equals 13, not 1. Hence, (4,1) is not a solution to the equation.
Step-by-step explanation:
The student made an error in reasoning that the point (4,1) is a solution to the equation y = 3x + 1 because they incorrectly switched the values of x and y. To find a solution to a linear equation, we substitute the x-value into the equation and solve for y, or vice versa. To verify whether (4,1) is a solution, we substitute x=4 into the equation and check if we get y=1.
To correct the student's error, let us do the substitution:
- Substitute x=4 into the equation: y = 3(4) + 1.
- Calculate the result: y = 12 + 1.
- Confirm if this is y=1: y = 13 (this is not equal to 1).
Since after substituting, we get y=13 and not y=1, we conclude that the point (4,1) is not a solution to the equation y = 3x + 1.