Linear Function (Graph)
A linear function is a mathematical function that can be represented by a straight line on a graph
A linear function is a mathematical function that can be represented by a straight line on a graph. It is often written in the form of y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line intersects the y-axis).
The graph of a linear function is a straight line that extends infinitely in both directions. The slope of the line determines its steepness or slope: a positive slope means the line goes up from left to right, while a negative slope means the line goes down from left to right.
The y-intercept, b, is the point where the line crosses the y-axis. It is the value of y when x is equal to 0. The y-intercept is important because it gives us a starting point to determine the position of the line on the graph.
To graph a linear function, you need at least two points on the line. You can find these points by substituting different x-values into the equation and solving for y. Once you have two or more points, you can plot them on the graph and draw a straight line that passes through them.
Linear functions are widely used in various fields of mathematics and science to model and analyze real-world situations. They are particularly useful when dealing with situations that involve proportional relationships, constant rates of change, or linear growth or decay.
In summary, a linear function is a mathematical function that can be represented by a straight line on a graph. It is characterized by its slope and y-intercept, and it is useful for modeling and analyzing real-world phenomena.
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