Final answer:
The slope indicates the rate of change of y with respect to x, and the y-intercept is the point where the line crosses the y-axis. In the equations provided, the slope is 4.83, which informs about the consistent rise over the run across the line, and the y-intercept is -173.5, indicating the starting point when x is 0.
Step-by-step explanation:
Understanding Slope and Y-intercept
To find the slope and y-intercept of a function, we can analyse its graphical representation or use two points from a table to calculate these values directly. Let's focus on understanding the definitions and interpretations first.
The slope of a straight line represents the rate of change, indicating how much the y-value (dependent variable) changes for a unit change in the x-value (independent variable). In a line equation y = mx + b, m stands for slope. A slope of 3 means that for every increase of 1 on the x-axis, there is a rise of 3 on the y-axis. The slope is consistent throughout the entire line.
The y-intercept is the point where the line crosses the y-axis, denoted as b in the equation. For instance, a y-intercept of 9 indicates that when x is zero, y is 9.
To illustrate with a provided equation, Y2 = -173.5 + 4.83x − 2(16.4) and Y3 = -173.5 + 4.83x + 2(16.4), it's clear that both lines will have the same slope as the line of best fit represented by the equation y = -173.5 + 4.83x. Thus their slope is 4.83, and their y-intercept is -173.5.
Understanding these concepts allows you to predict the behavior of the line and deduce valuable information such as trends, which is particularly useful in scenarios where the line represents a stock's performance over time.