In the earlier post we discussed about the importance of mathematics in Chemistry.Today,let us begin by understanding how we can plot our experimental data on a graph and represent our results pictorially.
In data representation ,straight line graphs are preferred as they show the data trends very clearly and thus we can get results on the graph without having to record them experimentally.So, we always try to get a straight line graph from the available data.
Every straight line can be represented by the equation , y = mx+ b ,where,
1.there are two variables –
i)y= dependent variable (See earlier post to know more about variables.)
ii)x= independent variable
2.there are two constants –
i)b= y-intercept i.e the point where the straight line meets the Y axis.
ii)m= slope/gradient of the line.
If the line passes through origin(0), then the equation of the lines becomes y=mx , as the y-intercept ,b=0.(see fig below)
SLOPE OF A LINE (m) –
Word ‘slope’ is derived from the Latin root ‘slupan’ meaning to slip or glide.The slope of the line is a measure of how steep the line is.So from the value of ‘m’, we get a sense of how slanting the line on the graph is.
Slope(m) = Change in y/Change in x = y2 – y1/x2-x1 = Rise/Run = dy/dx.
So what does the slope tell us ?
Slope of a line represents the change in y-value per unit change in x-value i.e it tells us the rate of change of y with respect to change in x.The larger the magnitude of the slope, the steeper the line is, i.e. the more it approaches the vertical.
If the line is –
i) more horizontal it means y is changing slowly with respect to change in x. Here, the value of slope is comparatively less which indicates that the line is more slanting.
ii) more vertical it means y is changing faster with little progressions in x . Here,the value of slope is comparatively more which indicates that the line is steep or less slanting.
iii)if the line is horizontal,parallel to X axis, it means the value of y is NOT changing with x.So, y2-y1 = 0, thus m= 0.Here, the slope is zero means the gradient or the rate of change is zero.
Slope can be negative , positive or zero.
i)Going from left end of the line to the right, if the line goes up then it’s a positive slope.It’s like going up the hill.
ii)Going from right end of the line to the left, if the line goes down, then its a negative slope.It’s like coming down the hill.
iii) Zero slope is like walking on a straight,flat ground.
So , the following graphs will exactly tell us how interpret graphs-
These concepts will be useful while studying the rates of reactions where we study the rate of change of concentration of reactants with time.
Point to remember → straight line representation of data helps us understand our experimental data better and thus scientists always strive to get the data on a straight line.
But what if we get a curve on the graph with our experimental data values? We shall try to discuss more on this in the next post. Till then ,
Be a perpetual student of life and keep learning…
Good day!
References and further reading –
1) https://en.wikipedia.org/wiki/Slope
2) https://www.mathsisfun.com/gradient.html
3) http://mathsfirst.massey.ac.nz/Algebra/StraightLinesin2D/Slope.htm
Image source –
1)https://www.montereyinstitute.org/courses/Algebra1/COURSE_TEXT_RESOURCE/U04_L1_T1_text_final_files/image014.gif
2) http://mathsfirst.massey.ac.nz/Algebra/StraightLinesin2D/Slope.htm
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