Final answer:
In algebra, the y-intercept is where a line crosses the y-axis and represents the starting value when x is zero. The slope indicates the rate of change of y with respect to x. In an equation like ŷ = 9 + 3x, the y-intercept is 9 and the slope is 3.
Step-by-step explanation:
Understanding the y-Intercept and Slope
The concept of the y-intercept is a fundamental aspect of algebra and coordinate geometry. The y-intercept represents the point where a line crosses the y-axis. This value, denoted commonly by "b" in the equation of a straight line (y=mx+b), indicates the value of y when x is zero. In linear models, the y-intercept can be interpreted as the starting value or initial condition of the relationship modeled by the line.
The slope is another critical concept in the study of linear equations. Represented by "m" in the linear equation format (y=mx+b), the slope indicates the rate of change of y with respect to x. It can be thought of as the inclination of the line, calculated as the rise over the run (change in y over change in x). In the context of a data set, the slope can represent the relationship's strength or the rate at which one variable changes in response to another.
When interpreting a line graph like the one illustrated in FIGURE A1 with an equation ŷ = 9 + 3x, the y-axis represents the dependent variable and the x-axis the independent variable. The y-intercept here is 9, meaning when x is zero, y is expected to be 9. The slope is 3, indicating that for every one unit increase in x, y increases by 3 units.