X-Y Plotting Operations > Slope

#### Slope

##### Calculating Instantaneous Rate of Change

An instantaneous rate of change for any point on an X-Y plot may be calculated. This is done by positioning the cross hair at the point of interest on the X-Y plot, then:

In the XY menu click on Slopes.

Choosing X-Y Slopes (ALT, X, S).

When the instantaneous rate of change function is activated, the analysis reporting area will display:

Where the value to the left of TNSLOPE is equal to the instantaneous rate of change between the points to the left and right of the point chosen (cross hair origin) in units of channel Y's units divided by channel X's units. For example, if channel X's Y-T waveform is calibrated in units of PSI and channel Y's in units of Liters, the rate of change is expressed in units of Liters/PSI.

##### Calculating 2-point and Linear Regression Rate of Change

Unlike the instantaneous rate of change, which calculates the rate of change at one point on a plot, the 2-point rate of change allows the slope of a line connecting two defined points on the X-Y plot to be determined. Linear regression rate of change reports the slope of a best-fit line between the two defined points. Both 2-point and linear regression rates of change are reported simultaneously in the analysis reporting area.

The two points over which the rates of change will be calculated are defined by moving the data cursor between the left and right limit cursors on the Y-T waveforms and enabling a time marker on window 1's (X channel) waveform. This defines the first point. The second point is defined by moving the data cursor to another point on the Y-T plot (the cross hair moves automatically on the X-Y plot). Note that cursor movement must be done with both “Scroll Lock” and “Caps Lock” off. Following your selection of the two points, the 2-point and linear regression rate of change is displayed in the analysis reporting area by:

In the XY menu click on Slopes.

Choosing X-Y Slopes (ALT, X, S).

When the 2-point and linear regression rate of change function is activated, the analysis reporting area will display:

Where the value to the left of LRSLOPE is the rate of change of the best-fit linear regression line and the value to the left of 2PSLOPE is the rate of change of a line intersecting the two defined points. In addition, a vector will be drawn on the X-Y screen connecting the two points over which the 2-point derivative is calculated. As with instantaneous rate of change, the derivative is presented in units of channel Y's units divided by channel X's units. For example, if channel X's Y-T waveform is calibrated in units of PSI and channel Y's in units of Liters, the rate of change is expressed in units of Liters/PSI.