A straight line is drawn through point A (-2; 3), parallel to the ordinate axis.

| August 15, 2021 | education

A straight line is drawn through point A (-2; 3), parallel to the ordinate axis. Which of the points lies on this line? 1) o (-2; -5) 2) d (-5; -2) 3) s (6; 3) 4) e (-6; 3)

A straight line drawn through point A (-2; 3) parallel to the ordinate axis (that is, the Ox axis) is a linear function of the form y = kx + b, where the slope k is zero. Therefore, the general form of the function y = b given in the task, in which b = 3, and x can take any values, but in this case they will not affect the value of y in any way, since it is constant, always equal to 3.

Properties of the function y = b
Although the function y = b is a special case of the linear function y = kx + b, their properties are different. Let’s consider and compare the properties of both functions.

Properties of the function y = kx + b:

The domain D (f) of the linear function у = kx + b is all real numbers: x ∈ (-∞; ∞).
The range of values ​​Е (f) of the linear function у = kx + b is also all numbers: у ∈ (-∞; ∞).
The function takes on the value 0 (y = 0) at x = -b / x.
The linear function y = kx + b increases for k> 0, decreases for k <0.
Properties of the function y = b:

The domain D (f) of the linear function y = b is all real numbers: x ∈ (-∞; ∞).
The range of values ​​E (f) of the linear function y = b is the number b: y = b.
There are no zeros in the function, since y never takes the value 0.
The linear function y = b does not increase or decrease.
Thus, only the domain of definition (1 property) is the same for both functions.

Determination of the membership of the points of the function y = b
Since the given function has the form y = 3, and x ∈ (-∞; ∞), then the graph of this function will belong to all points whose abscissa is equal to 3 (y = 3).

Points are given: 1) O (-2; -5), 2) D (-5; -2), 3) C (6; 3), 4) E (-6; 3).

Of these, points C and E have coordinates y = 3, so they lie on a straight line drawn through point A (-2; 3) parallel to the ordinate axis.

Answer: 3) C (6; 3), 4) E (-6; 3).



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