Based on the scatter plot, which equation represents the line best fit for the data about cups of beads?

Option B. y = 1.81x + 44.36

Step-by-step explanation:

The graph represents a scatter plot with a positive correlations and has a positive y-intercept.

By drawing the best line to fit the data the y-intercept will be approximately at the midpoint of 45 and 50

We will check which option is true:

A. y = 4.25 x

The equation of option A represents a line pass through the point (0,0)

Which mean y-intercept is 0 and this is wrong.

B. y = 1.81x + 44.36

According to the best line to fit the data option B is true.

Also by substitution with x = 2

y = 1.81 * 2 +44.36 = 47.98  

which is near to the actual point on the graph (50)

C. y = 1.81 x  ⇒ Wrong ⇒ same explanation of option A

D. y = 4.25 x + 50  ⇒ Wrong

Because the y-intercept will be approximately at the midpoint of 45 and 50

So, The answer is option B. y = 1.81x + 44.36

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

just sum

10 + 10 = 20