Linear relationship

Definition

A linear relationship is a relationship between two variables where the change in one variable is proportional to the change in the other. This relationship can be represented by a straight line on a graph using the equation $y = mx + b$.

5 Must Know Facts For Your Next Test

1. The slope ($m$) of the line indicates the rate of change between the variables.
2. The y-intercept ($b$) is the point where the line crosses the y-axis.
3. A positive slope means that as one variable increases, so does the other; a negative slope means that as one variable increases, the other decreases.
4. Linear relationships can be used to make predictions about data points not explicitly given.
5. The correlation coefficient ($r$) measures how well data fits a linear model, with $r = 1$ or $r = -1$ indicating a perfect fit.

Review Questions

• What does the slope of a linear relationship represent?
• How do you interpret the y-intercept in a linear model?
• What does it mean if two variables have a correlation coefficient of $r = -0.9$?

Related terms

Slope: The slope ($m$) represents the rate at which one variable changes with respect to another in a linear relationship.

Y-Intercept: The y-intercept ($b$) is the value of $y$ when $x=0$, representing where the line crosses the y-axis.

Correlation Coefficient: $r$ measures how well data conforms to a linear relationship, ranging from -1 to +1.