Final answer:
To graph the linear equation y = 4x + 2, plot the y-intercept at (0,2) and use the slope to find another point, such as (1,6). Draw a straight line through these points. Similar methods apply to graphing the line of best fit and associated equations, utilizing graphing tools or a table of values.
Step-by-step explanation:
To graph the equation y = 4x + 2, you need to understand that it is in slope-intercept form, where the slope (m) is 4 and the y-intercept (b) is 2. Start by plotting the y-intercept on the graph at (0,2). Then, use the slope to determine another point. Since slope is rise over run, you will move up 4 units and to the right 1 unit from the y-intercept to find a second point at (1,6). Plot this point as well.
Once you have these two points, you can draw a straight line through them to represent the graph of y=4x+2. This line will continue infinitely in both directions, and every point on the line is a solution to the equation. To graph lines of best fit and their related confidence intervals, such as Y2 = -173.5 + 4.83x - 2(16.4) and Y3 = -173.5 + 4.83x + 2(16.4), the process is similar, but focuses on using a graphing calculator or software. You enter these equations into the program, plot the resulting points, and draw the line for each equation.
Equations like y = 9 + 3x can also be graphed using a table of values where you substitute different x-values into the equation to find corresponding y-values. These pairs are plotted on the graph to draw the line. In summary, graphing linear equations involves identifying the y-intercept and slope, plotting points, and drawing a line through these points to visualize the equation.