Final answer:
A linear relationship can be identified by an equation in the form y = mx + b or y = b + mx, where m is the slope and b is the y-intercept. If the data, when graphed, results in a straight line, this indicates a linear relationship. Otherwise, it is not linear.
Step-by-step explanation:
You can determine if it’s a linear relationship by looking at the equation of the relationship or by graphing the data. If the equation of the relationship takes the form y = mx + b or y = b + mx, where m and b are constants, and x is the independent variable, then it is a linear relationship. The graph of this equation will result in a straight line, showing a direct relationship between the variables.
The slope, represented by m in the equation, indicates the rate of change between the dependent and independent variables. If the slope is positive, the line goes up as it moves from left to right; if the slope is negative, the line goes down. The y-intercept, represented by b, is where the line crosses the y-axis. This is the value of y when x is zero.
Professionals use these linear equations to understand the relationship between two numerical variables, for example, exam scores. If the relationship is not represented by a straight line when graphed, it is not a linear relationship but could be quadratic, inverse, or exponential as shown in different graphs.