Final answer:
To address the question, draw a scatter plot for the given data points to identify any pattern, determine the appropriateness of a linear model, describe the correlation, draw a trend line, provide its equation, and predict future values.
Step-by-step explanation:
To draw a scatter plot for the given set of data points: (3, 5), (4, 7), (5, 9), (7, 10), (8, 10), (9, 11), and (10, 13), plot each point on a graph where the x-axis represents the independent variable and the y-axis represents the dependent variable. Once plotted, look for a pattern to determine if a linear model is appropriate.
If the data points line up in a way that suggests a straight line could be drawn through them, then a linear model is considered suitable. By inspection, if there is a consistent upward trend without significant deviations from a straight path, the relationship can be described as positively correlated. A trend line added to the scatter plot can represent the line of best fit, and the equation can be calculated using the least-squares method, often written in the form ý = a + bx.
To predict the value of y when x is 15, extend the line of best fit beyond the existing data points if the linear model is valid and use the equation to calculate the corresponding y value. Note that such an extrapolation assumes that the linear relationship continues beyond the range of the provided data.