The scatter plot below shows the profit earned each month by a new company over the first year of operation.
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The owner writes a line of best fit equation, shown below, to model the relationship between profit earned and month.
y = 2,500x - 2,500
Explain how you know that the line of best fit equation is appropriate, mentioning both the slope and y-intercept in your response.
You don't have to explain if you don't want to, but I would please at least like the slope/y-intercept and equation.
The line of best fit equation is y = 2500x - 2500, and it is appropriate as a model for the profit earned each month by this new company.
The slope of the line is 2,500, which represents the approximate increase in profit each month. From the scatter plot, we can observe that the profit tends to increase linearly with the increase of the month number. The slope (2,500) captures this trend by showing that the profit is increasing at a rate of $2,500 per month.
The y-intercept of the line is -2,500, which represents the starting point or the profit at the beginning of the first month (month x = 0). From the scatter plot, we can observe that the profit at the start is slightly negative, meaning the company might have incurred some initial costs or losses. The y-intercept (-2,500) captures this fact by showing that the profit starts at -$2,500 in the first month.
Considering both the slope and y-intercept, the line of best fit equation (y = 2500x - 2500) is appropriate as it accurately models the general trend of increasing profit over time and captures the initial losses experienced by the company.
The line of best fit equation given for the scatter plot is:
y = 2,500x - 2,500
To determine if this equation is appropriate, we need to consider the slope and the y-intercept.
1. Slope (2,500): The slope represents the rate of change, indicating how much the y-value (profit) changes for each unit increase in the x-value (month). In this case, the slope is positive (2,500), which suggests that as the month increases, the profit earned also increases. This aligns with the positive trend observed in the scatter plot, where the points generally move upwards from left to right.
2. Y-intercept (-2,500): The y-intercept represents the value of y (profit) when x (month) equals zero. In this equation, the y-intercept is -2,500, indicating that the company had a profit of -2,500 in the first month. While it is unusual to have a negative profit at the beginning, it could be due to initial startup costs or other factors specific to this company.
Considering the positive slope and the y-intercept, the line of best fit equation seems appropriate for this scenario as it reflects the increasing trend in profit over the first year of operation.
To determine if the line of best fit equation is appropriate for the scatter plot, we need to consider the slope and y-intercept.
The slope of the line, represented by the coefficient next to 'x' in the equation, is 2,500. In this case, the slope indicates that for every month that passes (change in 'x'), the profit earned (change in 'y') increases by 2,500 units. This positive slope suggests a positive correlation between the month and profit earned, meaning that as time goes on, the company's profit tends to increase.
The y-intercept, represented by the constant term in the equation, is -2,500. It is the point where the line intersects the y-axis. In this context, it indicates that in the first month (x=0), the company would have a profit of -2,500 units. This implies that the company started with a loss of 2,500 units before earning any profit.
The equation itself, y = 2,500x - 2,500, represents a linear relationship between the month and profit earned. It suggests that the best-fit line passes through a point (-2,500, 0) and has a slope of 2,500.
To verify the appropriateness of the line of best fit equation in this scenario, it is crucial to consider other factors such as the overall distribution of the data points, the possible presence of outliers, and the relationship between profit and time. The line is considered the best fit if it reasonably represents the general trend of the data and minimizes the sum of the squared differences between the observed data points and the predicted values on the line.