Final answer:
The question addresses graphing linear equations, focusing on slope, y-intercept, and best-fit lines. An example equation provided shows how to calculate total labor charges based on hours worked. Graphing a best-fit line on a calculator helps visualize the data's linear relationship.
Step-by-step explanation:
The question provided seems to be concerned with analyzing a linear equation and its graphical representation, particularly focusing on the concepts of slope, y-intercept, and best-fit lines. In Graphing Linear Equations, the y-intercept is the point where the line intersects the y-axis, and the slope represents the steepness of the line, indicating the rise over the run (change in y over change in x).
One example given is the equation y = 55x + 75, where the slope is 55 (indicating that for every hour worked on a car, the labor charge increases by 55 dollars), and the y-intercept is 75 (the initial charge to fix the car). If we apply this to 3.5 hours of labor, the total cost would be calculated as y = 55(3.5) + 75, resulting in a total of 267.50 dollars.
To graph a best-fit line, such as y = -173.5 + 4.83x, one would insert the equation into a graphing calculator and use the appropriate zoom setting to visualize the line. This process assists in understanding how well the line fits the given data points.
To find the slope of the line, you need to determine the rate of change between two points on the graph. The slope in this case is 3, which means there is a rise of 3 on the vertical axis for every increase of 1 on the horizontal axis.
The equation that represents the line on the graph is ŷ = -266.8863 + 0.1656x. This equation allows you to calculate the y-value (ŷ) for any given x-value on the line.