For this case we have that by definition, the point-slope equation of a line is given by:
Where:
It is a point through which the line passes
m: It is the slope of the line
According to the data we have to:
Substituting:
Finally, the equation of the line is:
ANswer:
Answer:
Step-by-step explanation:
For the set of points that include all solutions are
such that
; then we have
.
What is important to stress here is that represents all of the solutions, while other points that we are given represent one solution (for example, point (2,-1) is just one solution)
The quadratic regression equation that best fits the data set is y = 32.86x² - 379.14x + 1369.14
<h3>The data points </h3>The following table of values represents the data points that would be used to solve this question:
x 3 4 5 6 7 8 9
y 470 416 403 226 314 338 693
Where:
The table of values illustrates a quadratic function.
The function would be calculated using a graphing calculator
From the graphing calculator, we have:
a = 32.86; b = -379.14 and c = 1369.14
A quadratic regression equation is represented as:
y = ax² + bx + c
So, we have:
y = 32.86x² - 379.14x + 1369.14
Hence, the quadratic regression equation that best fits the data set is y = 32.86x² - 379.14x + 1369.14
<h3>Why the function type was chosen?</h3>From the table of values in (a), we can see that as x increases; the value of y decreases and then increases after it reaches a minimum.
This illustrates the behavior of a quadratic regression function
See attachment for the scatter plot
Read more about quadratic regression equation at:
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