Solve each problem. The graph shows a straight line that...

Solve each problem. The graph shows a straight line that approximates the percentage of Americans 25 years and older who had earned bachelor's degrees or higher for the years $1990-2012 .$ Use the midpoint formula and the two given points to estimate the percent in 2001 . Compare the answer with the actual percent of 26.2. (GRAPH CANNOT COPY)

Solve each problem.
The graph shows a straight line that approximates the percentage of Americans 25 years and older who had earned bachelor's degrees or higher for the years $1990-2012 .$ Use the midpoint formula and the two given points to estimate the percent in 2001 . Compare the answer with the actual percent of 26.2.
(GRAPH CANNOT COPY)

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Key Concepts

Interpolation

Interpolation is a technique used to estimate unknown values that fall within the range of a set of known data points. When the data is linear, as in this case, linear interpolation allows one to calculate a value at any intermediate point by proportionally scaling the difference between the two endpoints.

Midpoint Formula

The midpoint formula, typically expressed as (x1 + x2)/2 for the x-coordinate and (y1 + y2)/2 for the y-coordinate, identifies the point exactly in between two given points. In the context of linear models, it can be employed to estimate a value at the midpoint of an interval when the relationship is linear.

Linear Functions

A linear function describes a relationship where the rate of change between the variables is constant, resulting in a straight-line graph. This concept is fundamental when estimating values since it allows one to use the known points on the line to predict intermediate or future values.

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