Mastering Graphing Linear Functions: Slope, Y-Intercept And Graphing Techniques

graph of a linear function

the most basic function in a family of functions

A linear function is a function that can be represented by a straight line on a coordinate plane. It is a type of function where the output is directly proportional to the input.

The standard form of a linear function is y = mx + b, where m is the slope or gradient of the line and b is the y-intercept. The slope determines the steepness of the line, while the y-intercept is the point where the line crosses the y-axis.

To graph a linear function, you need to plot two points on the coordinate plane and then draw a straight line through them. One easy way to do this is to use the slope-intercept form of the equation, which gives you the y-intercept and the slope of the line.

For example, let’s say you have the equation y = 2x + 1. To graph this function, you can start by plotting the y-intercept, which is (0, 1). This means that when x is equal to 0, the value of y is 1.

Next, you can use the slope, which is 2, to find another point on the line. The slope tells you how much y changes for every unit of x. In this case, when x increases by 1, y increases by 2. So if you start from the y-intercept of (0, 1) and move up 2 units and right 1 unit, you will get the point (1, 3).

Now that you have two points on the line, you can draw a straight line through them. This will give you the graph of the linear function y = 2x + 1.

More Answers: