The equation that best models the considered data set is given by: Option A: y = -(3/4)x + 6
It is called regression. It can be linear regression (in which we fit a line to the set of data), or polynomial regression(in which we fit a higher degree curve to the set of data considered).
For this case, we see that the data is such that a line would be a good model to predict it.
The line would touch the x axis somewhat near x=6 or 7, and on the y-axis it would touch near to 5 to 8 (just visualizing and predicting).
So, this eliminates the option B, C and D as in a line segment [tex]y =mx + c[/tex], the value c represents the value of y-intercept it makes (ie the line [tex]y =mx + c[/tex] intersects the y-axis at y = c).
We will use the fact that one option is true, and that B, C and D are not true so option A is correct. Its slope -(3/4) also fits the line as slope is negative showing the line leaning on left side, and the value 3/4 is approx 1, showing that as at y = 0 x is approx 7, so as at x = 0, y is approx 7.
The accurate method would be to fit a line using least squares method, but for that we'd need the correct coordinates of the point( which are not accurately predictable from image).
Thus, the equation that best models the considered data set is given by: Option A: y = -(3/4)x + 6
Learn more about linear regression here:
https://brainly.com/question/18854090
