Final answer:
The slope represents the rate at which one variable changes in relation to another. Positive slopes indicate a direct relationship, and negative slopes indicate an inverse relationship.
Step-by-step explanation:
To find the slope of a line, which represents how one variable changes in relation to another, we can use the concept that slope is the rate of change between two points. The slope can be calculated by finding the difference in the y-values divided by the difference in the x-values between two points on a line graph.
Examples:
- (a) A slope of 1/20 means the number of gas increases by 1 gallon for every 20 miles driven. This is a positive slope, indicating a direct relationship between the two variables.
- (b) A slope of -20 suggests that the number of gas decreases by 20 gallons for every mile driven. This is a very steep negative slope, showing an inverse relationship between the two variables.
- (c) A slope of -1/20 describes a situation where the number of gas decreases by 1 gallon every 20 miles. This negative slope is less steep, meaning the decrease in gas is more gradual compared to example (b).
- (d) A slope of 20 indicates the number of gas increases by 20 gallons for every mile, which is an extremely steep positive slope.