The equation of a straight line is often written as: y = mx + c Rearrange this equation to make x the subject.
x = y / m - c
x = y - c / m
x = (y - c) / m
x = c - y / m
In Excel, the slope and intercept of a ‘best-fit’ straight line for a set of experimental data points (x-data and y-data) can be calculated by using the functions, SLOPE(y-data,x-data) and INTERCEPT(y-data,x-data). What function can be used to calculate the slope of a ‘best-fit’ straight line that must also pass through the origin (0,0) of the graph.
ORIGIN(y-data,x-data)
LINE(y-data,x-data,0,0)
SLOPE(y-data,x-data,0,0)
LINEST(y-data,x-data,FALSE,FALSE)
The cooking time, t (min), for a particular joint of meat of ‘weight’, w (kg), is given as 20 minutes per 0.5 kg plus 30 minutes, which can be represented by a straight line equation. t = mw + c The values for the slope and intercept of this straight line are then:
Slope, m = 40 and intercept, c = 30
Slope, m = 20 and intercept, c = 30
Slope, m = 30 and intercept, c = 20
Slope, m = 60 and intercept, c = 20
The calibration of an atomic absorption measurement gives a linear response of absorption, A, over a short range of concentration values, C (in ppm), represented by the equation: A = 0.348C + 0.022 Calculate the concentration (to 2sf) of the solution that produces an absorbance of A = 0.263.
0.82
0.71
0.81
0.69
A calibration table of the voltages, E, from a type J thermocouple as a function of temperature, T, gives E = 5.27 mV at T = 100.0 C and E = 5.81 mV at T = 110.0 C.. Assuming a linear response of voltage against temperature between these values, calculate the temperature (to 4 sf) of the thermocouple if it shows a voltage of E = 5.65 mV.