Mathematics of Linear Relationships

The mathematical equation representing a straight-line relationship between variables x and y is as follows  

If the variables x and y bear a linear relationship to one another, then m and b are constants defining the slope (m) of the line (how steep it is) and the y-intercept (b), the value of y when x is zero. The slope of a line can be determined very simply if two or more points, (x, y,) and (x2, y2), that make up the line 

The y-intercept can be determined by observing what the y value is on the graph where the line crosses the y-axis, or if the slope and one point are known, it may be calculated using Equation (6.6). 

The important observation for instrumental analysis is that the K in Equation (6.1) is the same as the m in Equation (6.6). Thus, in a graph of R vs. C, the slope of the line is the K value, the proportionality constant. 

It would seem that the y-intercept would always be zero, since if the concentration is zero, the instrument readout would logically be zero, especially since a blank is often used. The blank, a solution prepared so that all sample components are in it except the analyte (see Section 6.6), is a solution of zero concentration. Such a solution is often used to zero the readout, meaning that the instrument is manually 

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