Final answer:
The slope represents the rate of change of the dependent variable with respect to the independent variable, while the y-intercept illustrates the value of the dependent variable when the independent variable is zero. A positive slope indicates a direct relationship between the two variables.
Step-by-step explanation:
The slope of a line, often represented by the letter m, indicates the rate at which the dependent variable changes with respect to the independent variable. In the context of a temperature increase, the slope would represent the change in temperature (rise) per unit change in time (run). For instance, if the slope is 3, it indicates that for every one unit increase in time, the temperature rises by 3 degrees.
The y-intercept, represented by the letter b in the equation of a line, shows the value of the dependent variable when the independent variable is zero. For example, if a line graph has a y-intercept of 9, this means when the time is zero, the temperature is already at 9 degrees. It is the starting point of the line when plotted on a graph.
In summary, understanding both the slope and the y-intercept is crucial for interpreting linear relationships in various fields, such as economics, where they can describe relationships between two variables like price and quantity supplied. A positive slope suggests a direct relationship where both variables increase or decrease together, reflecting a rising line on a graph.