Students' mistakes are defined as follows
Consider that the correspondence between the value x = 2 and the y values of the vertical axis is a function.
They ignore the role of the fixed term in the linear function y = -3x, ie they ignore that the graphical representation of the linear function y = -3x is a straight line passing from the beginning of the axes.
They ignore the sign of α and β, α <0 and β <0 on the linear function y = -3x-2
The graphical representation is a straight line that intersects the vertical negative half-axis and forms an angle with the horizontal axis greater than 90 degrees.
They ignore the sign of the α and β, α> 0 and β <0 coefficients in the linear function y = 3x-1The graphical representation is a semicircle that intersects the vertical negative half-axis and forms an angle with the horizontal axis less than 90 degrees.
They ignore the sign of α and β, α <0 and β> 0 on the linear function y = -2x + 1, -2≤x≤2
The graphical representation is a straight line that intersects the vertical positive half-axis and forms an angle with the horizontal axis greater than 90 degrees.
They ignore the verbal expression of every kilo of olive oil produced in 0.2 kilograms of oil, a ratio between the amount of y kg of oil and the quantity of kilos of olives. They do not know that the above verbal relationship is represented by a price table.
They do not know how the representation of the above ratio of y and x is transferred from the value table to the algebraic form of the function y = 0,2x
They do not know that the straight line passing from the beginning of the axes and forming an angle of less than 90 degrees is given by the algebraic formula y = αx, α> 0
They do not know that the straight line passing from the beginning of the axes and intersecting the positive vertical axis and forming an angle of less than 90 degrees is given by the algebraic formula y = αx + β, α> 0, β> 0
Consider that the correspondence between the value x = 2 and the y values of the vertical axis is a function.
They ignore the role of the fixed term in the linear function y = -3x, ie they ignore that the graphical representation of the linear function y = -3x is a straight line passing from the beginning of the axes.
They ignore the sign of α and β, α <0 and β <0 on the linear function y = -3x-2
The graphical representation is a straight line that intersects the vertical negative half-axis and forms an angle with the horizontal axis greater than 90 degrees.
They ignore the sign of the α and β, α> 0 and β <0 coefficients in the linear function y = 3x-1The graphical representation is a semicircle that intersects the vertical negative half-axis and forms an angle with the horizontal axis less than 90 degrees.
They ignore the sign of α and β, α <0 and β> 0 on the linear function y = -2x + 1, -2≤x≤2
The graphical representation is a straight line that intersects the vertical positive half-axis and forms an angle with the horizontal axis greater than 90 degrees.
They ignore the verbal expression of every kilo of olive oil produced in 0.2 kilograms of oil, a ratio between the amount of y kg of oil and the quantity of kilos of olives. They do not know that the above verbal relationship is represented by a price table.
They do not know how the representation of the above ratio of y and x is transferred from the value table to the algebraic form of the function y = 0,2x
They do not know that the straight line passing from the beginning of the axes and forming an angle of less than 90 degrees is given by the algebraic formula y = αx, α> 0
They do not know that the straight line passing from the beginning of the axes and intersecting the positive vertical axis and forming an angle of less than 90 degrees is given by the algebraic formula y = αx + β, α> 0, β> 0
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