Final answer:
The correct answer is that the slope of the line graph is 3, indicating a rise of 3 units on the y-axis for every 1 unit increase on the x-axis, and the y-intercept is 9.
Step-by-step explanation:
The slope of a graph represents the rate of change between the independent (x) and dependent (y) variables, which is important in understanding the relationship between these two variables in various contexts, such as rate of payments, motion, or growth. Given the information from Figure A1 regarding the slope and the Algebra of Straight Lines, the correct answer is that the slope of the line graph is 3. This means there is a rise of 3 on the vertical axis for every increase of 1 on the horizontal axis. Furthermore, the y-intercept is 9, indicating where the line crosses the y-axis. This straight line's equation would generally have the form y = mx + b, with m representing the slope and b representing the y-intercept.
The slope of a line is a value that describes the rate of change between the independent and dependent variables. The slope tells us how the dependent variable (y) changes for every one-unit increase in the independent (x) variable, on average. The y-intercept is used to describe the dependent variable when the independent variable equals zero.
For example, if the slope of a graph is 3, that means there is a rise of 3 on the vertical axis for every increase of 1 on the horizontal axis. This indicates that the dependent variable is increasing at a rate of 3 units for every one-unit increase in the independent variable.