Q:

What is a linear relationship in math?

A:

A linear relationship in mathematics is one in which the graphing of a data set results in a straight line. The formula y = mx+b is used to represent a linear relationship. In this formula m is the slope of the line, and b is the X-intercept. The graph of distance traveled versus time, at a constant speed, is a linear relationship.

A linear relationship with a slope of 1 and that begins at the origin of the graph is a direct proportion. This indicates that a change of one unit on the X axis of the graph results in a change of one unit on the Y axis. However, as shown by the formula for a linear relationship, the slope is not limited to 1. In addition, all graphs do not begin at the origin. In linear relationships with a negative slope, the y value decreases as the x value increases.

Science uses graphs to represent data sets. While there is a possibility for individual data points, collected from an experiment, to vary somewhat from the line, statistical analysis is useful in determining the best fit of a line. Once the scientist determines the line, he uses it to interpolate data for points not collected in an actual experiment.

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