Final answer:
The slope and y-intercept are critical in defining the characteristics of a straight line on a graph. The slope is 3, indicating a steepness of 3 units up for every 1 unit along the x-axis, while the y-intercept is 9, showing where the line crosses the y-axis. Together, they help in graphing and understanding the line's equation.
Step-by-step explanation:
When we discuss the slopes and y-intercepts of line graphs, we're referring to fundamental concepts in algebra that describe the characteristics of straight lines on a coordinate plane. The slope of a line is the measure of its steepness and direction. For the line represented in Figure A1, the slope is 3, which means for each unit the independent variable (x) increases, the dependent variable (y) increases by 3 units. This 'rise over run' reflects the rate of change between the two variables.
The y-intercept is the point where the line crosses the y-axis. In Figure A1, the y-intercept is 9, which indicates that when x is 0, y equals 9. This point is particularly important because it helps to anchor the line on the graph, providing a starting point for constructing the line when graphing or understanding where the line will be when the independent variable is zero.
In algebraic terms, the equation of the line can be written as y = mx + b, where m represents the slope and b represents the y-intercept. These two values, slope and y-intercept, determine the shape and position of the line on the graph. This is a central aspect of understanding the relationship between the equation of a line and its graphical representation.