Linear Function Equation
A linear function is a type of function in which the rate of change between the dependent variable and independent variable is constant
A linear function is a type of function in which the rate of change between the dependent variable and independent variable is constant. It forms a straight line when graphed on a coordinate plane.
The equation of a linear function is usually written in the form of y = mx + b, where:
– y represents the dependent variable,
– x represents the independent variable,
– m represents the slope of the line, and
– b represents the y-intercept (the point where the line crosses the y-axis).
Let’s break down the components of the linear function equation:
1. Slope (m):
The slope of a line determines its steepness or its rate of change. It represents how much y changes for every unit change in x. The slope can be positive, negative, or zero. If the slope is positive, the line slopes upward from left to right; if it is negative, the line slopes downward. A zero slope represents a horizontal line. You can find the slope by comparing two points on the line using the formula: m = (y2 – y1) / (x2 – x1), where (x1, y1) and (x2, y2) are two points on the line.
2. Y-intercept (b):
The y-intercept is the point where the line crosses the y-axis (when x is equal to zero). It indicates the starting value of y when x is zero. To find the y-intercept, you can look at the equation and determine the value of y when x is zero.
Example:
Let’s say we have the equation y = 2x + 3.
In this equation, the slope is 2 because the coefficient of x is 2. This means that for every 1 unit increase in x, y increases by 2 units.
The y-intercept is 3 because it is the value of y when x is zero. So, when x is zero, y is 3.
To graph this linear function, you can start by plotting the y-intercept at (0, 3) on the coordinate plane. Then, using the slope of 2, you can find another point by moving 1 unit to the right and 2 units up from the y-intercept. Connect the two points with a straight line, and you have graphed the linear function.
I hope this explanation helps! If you have any more questions or need further clarification, feel free to ask.
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