Interpreting linear relationships quick check
1. What is a linear relationship?
A linear relationship is a type of relationship where the change in one variable is directly proportional to the change in another variable. This means that when one variable increases or decreases, the other variable also increases or decreases at a constant rate.
2. How can you tell if a scatter plot shows a linear relationship?
You can tell if a scatter plot shows a linear relationship by examining the pattern of the data points. If the points form a straight line or cluster around a straight line, then the relationship is likely linear. You can also calculate the correlation coefficient (r) to determine the strength and direction of the relationship.
3. How can you interpret the slope of a line in a linear relationship?
The slope of a line in a linear relationship represents the rate of change between the two variables. A positive slope indicates a positive relationship, where as one variable increases, the other variable also increases. A negative slope indicates a negative relationship, where as one variable increases, the other variable decreases. The magnitude of the slope also indicates the steepness of the relationship.
4. How can you interpret the y-intercept of a line in a linear relationship?
The y-intercept of a line in a linear relationship represents the value of the dependent variable (y) when the independent variable (x) is equal to zero. It is the point where the line intersects the y-axis. The y-intercept can give insight into the initial value or starting point of the relationship.
5. What are some real-life examples of linear relationships?
Some real-life examples of linear relationships include the relationship between time and distance traveled at a constant speed, the relationship between temperature and gas volume in a closed container at constant pressure, and the relationship between number of hours worked and earnings at an hourly rate.