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