Question

the following readings were obtained in an experiment.
X |4.00|4.75|5.25|6.00|6.75|7.50|8.00
Y |1.75|3.00|3.50|3.75|5.00|5.25|6.25
a. plot a graph of Y against X, use 1cm to represent I unit on both axis
b. measure the gradient
c. estimate the error in the gradient
d. measure the Y intercept

Answer 1

a.

b. From the graph, the gradient is given by

$gradient=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{5.95-2.75}{7.9-4.77}=1.02$

c. By using micosoft excel, the error can be calculated

The error is 0.1534. The procedure for calculating the error can be learnt from this video: https://youtu.be/eV-RKGGrtA8

d. As seen on the graph, the equation of the chart is y = 1.0235x - 2.106. By comparing this to the equation of a straight line, y=mx + c, where m is the slope and c is the y-intercept; -2.106 is the intercept of the slope.