Graphing of a Linear Function
We know that graph of linear equation represents the straight line and to draw a straight line we need at least two point and joining those two points and stretching the line in both the direction gives the required straight line. The graph of a linear function f(x) = mx + b is shown in the image added below as,
Case 1: When m > 0
The image added below shows the linear function when m > 0,
Case 2: When m < 0
The image added below shows the linear function when m < 0,
Case 3: When m = 0
Graphing a Linear Function by Finding Two Points
To discover two pinpoints on a linear function (line) f(x) = mx + b, consider some unexpected values for ‘x’ and have to replace these values to find the connected values of y.
This method is presented by an instance where we are proceeding to graph the function f(x) = 2x + 4.
Step1: Find two points on the line by first taking two random value of x
x = 0 and x = 1
Step2: Find the value of the y with the respective value of the x.
x | y |
---|---|
0 | 2(0) + 4 = 4 |
1 | 2(1) + 4 = 6 |
So, the two points on the line are (0, 4) and (1, 6).
Step 3: Plot the point on the graph and join them to get the graph of required linear function.
Graphing of Linear Function Using Slope and Y-intercept
To graph a linear function using slope and y-intercept form, we first the linear function in the standard slope as,
f(x) = mx + b
where, m is slope of line and the y intercept is b. For example,
f(x) = 2x + 4
- slope of line = 2
- y-intercept = 4
- point on y-axis = (0, 4)
Now to find plot the line we follow the steps added below,
Step 1: Firstly Plot the y-intercept (0, b) i.e. (0, 4)
Step 2: Now the slope in fraction is represented as rise/run
Here,
slope = 2 = 2/1 = rise/run
So, rise = 2 and run = 1
Step 3: Rise the y-intercept vertically by “rise” and then run horizontally by “run”. This results in a new point.
Here, we move 2 units vertically in the direction of y-axis and move horizontally 1 unit in direction of x-axis.
Step 4: Now join the points from Step 1 and Step 3 we get the required graph of linear function.
Linear Function
A linear function is a mathematical function that creates a straight line when graphed. It can be described by the formula: y = mx+b. A linear function in Algebra represents a straight line in the 2-D or 3-D cartesian plane. Hence this function is called a linear function. It is a function with variables and constant but no exponent value.
A linear function is represented as y = mx + c where y is the dependent variable and x is the independent variable. We know that for any function y = f(x) linear functions are also represented as, f(x) = mx + c
Let’s know more about Linear Function, Examples of Linear Function, equation and the graph of Linear function below.