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"For the next generation"
© 2025 Astra.si. All rights reserved.
"For the next generation"
A linear function is a mathematical expression that describes a relationship between two variables where one variable is linearly dependent on the other. The general form of a linear function is f(x) = mx + b, where 'm' represents the slope of the line, and 'b' represents the initial value or the y-intercept. The graph of a linear function is always a straight line, which means that a change in one variable causes a uniform change in the other.
Linear functions are a fundamental part of mathematics, often used to describe simple, linear relationships in various contexts. This form of the equation shows that the y-coordinate is linearly dependent on the x-coordinate.
The graph of a linear function is a straight line, which can be drawn if we know two points on it. Let's see how to do this:
The point on the graph where the line intersects the y-axis is (0, b). The point (0, b) tells us the value of y when x is equal to zero.
The slope 'm' tells us how steep the line is. If 'm' is positive, the line rises from left to right; if 'm' is negative, it falls.
This determines the steepness of the line. If m > 0, the line rises. If m < 0, the line falls. If m = 0, the line is horizontal.
This determines where the line intersects the y-axis. It is the value of the function when x = 0.
The graph of a linear function is always a straight line.
Linear functions are an essential part of mathematics, enabling the understanding of many basic and advanced concepts. Their simplicity and versatility allow for wide application in various scientific and everyday situations.
