Final answer:
The student is likely inquiring about an equation for a red graph derived from data points and linear regression. They are expected to use a linear equation to plot a regression line on a scatter plot to visualize the relationship between the variables.
Step-by-step explanation:
The student is asking for the equation of a red graph that corresponds to a given black graph of y=f(x). Without more specific information or an image, it's difficult to provide the exact equation for the red graph. However, the reference to a regression line suggests the student may be working with linear regression, which is a method used to define a linear relationship between data points in the form of a line of best fit.
When plotting a line, one must be aware of the slope and y-intercept provided by the linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept. For example, the equation -173.5 + 4.83x would represent a line with a slope of 4.83 and a y-intercept of -173.5.
The points mentioned, such as (4,2), along with instructions on how to use a calculator to add a regression line to a scatter plot, imply that the question focuses on understanding how to plot and interpret the linear equations and their corresponding graphs. For a specific equation, you would substitute the variables with actual values and calculate the corresponding y to determine the graph's accurate representation on a coordinate plane.