Answer :
The function that models the relationship between the two points is y = 2.5x + 95, which is option D. To determine the function that models the relationship between the two points (2, 100) and (4, 105), we will make use of the slope-intercept form of a linear equation.
The slope-intercept form of the linear equation is given by:y = mx + b
where m is the slope of the line, and b is the y-intercept of the line.
To find the slope, we use the slope formula which is given as:
m = (y₂ - y₁) / (x₂ - x₁)
Where (x₁, y₁) = (2, 100) and (x₂, y₂) = (4, 105).
m = (105 - 100) / (4 - 2)
m = 5/2 = 2.5
So, the slope of the line is 2.5.
Now we substitute the slope and one of the points (2, 100) into the slope-intercept form of the linear equation to find the y-intercept, b.100 = 2.5(2) + b
100 = 5 + b
b = 100 - 5
b = 95
Thus, the function that models the relationship between the two points is y = 2.5x + 95, which is option D.
To learn more about slope-intercept, refer:-
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