RATE OF CHANGE OF THE LINEAR FUNCTION

Опубликовано: 04 Май 2026
на канале: MATEMÁTICA com Jonnys Calvet

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RATE OF CHANGE OF A LINEAR FUNCTION

Coefficients of the linear function. Descriptor 7

In a first-degree function, the rate of change is given by the coefficient a. We know that a first-degree function follows the following formation law: f(x) = ax + b, where a and b are real numbers and b ≠ 0.

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Let's prove through a proof that the rate of change of the function f(x) = 2x + 3 is given by 2.

f(x) = 2x + 3
f(x + h) = 2 * (x + h) + 3 → f(x + h) = 2x + 2h + 3 (h ≠ 0)

Therefore, we have:

f(x + h) − f(x) = 2x + 2h + 3 – (2x + 3)

f(x + h) − f(x) = 2x + 2h + 3 – 2x – 3
f(x + h) − f(x) = 2h

This is one of the most important topics in mathematics for the ENEM and other university entrance exams.

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Reference Matrix – Mathematics – 3rd year of high school
DESCRIPTOR OF THE BRAZIL TEST
D6 – Identify the location of points on the Cartesian plane. D7 – Interpret geometrically the coefficients of the equation of a line.

D8 – Identify the equation of a line given two points or a point and its slope.
D9 – Relate the determination of the intersection point of two or more lines to the solution of a system of equations with two unknowns.
D18 – Recognize an algebraic expression that represents a function from a table.
D19 – Solve problems involving first-degree functions.
D20 – Analyze growth/decrease and zeros of real functions shown in graphs.
D21 – Identify the graph that represents a situation described in a text.
D23 – Recognize the graph of a first-degree polynomial function through its coefficients.
D24 – Recognize the algebraic representation of a first-degree function, given its graph.

Professor Jonnys Calvet
GRADUATION: State University of Maranhão (UEMA). Postgraduate Studies: Brazilian Institute of Capital Markets (IBMEC).