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Let us consider a particle motion with constant speed v .  Hence particle position x with time t is given by

where x_o is initial position .

Let us consider following data

The above data is plotted as given below . The graph above data is linear or striaght line.

If we extend the line to meet y-axis , then the point of intersection of graph and y-axis is y-intercept.

In above graph , if we extend the graph to meet y-axis , we get y-intercept 10 m .

Hence at t = 0 ,position of particle is 10 cm .

To get slope of graph , let us fix two points on graph and draw right triangle so that line between two fixed points is

hypotenuse of right triangle . Then the ratio of value of vertical line to the value of horizontal line is slope .

In the above graph , let us fix point A and point C and draw the right triangle as shown in figure so that

line segment between A and C is hypotenuse.

Then slope = ΔS/Δt = [ (40-20) m / (6-2) s ] = 5 m/s