Question #3efc2

1 Answer
Apr 19, 2016

Gradient is the slope of a graph at point of interest.
For straight line graph it remains same. For curves, it changes as per location of the point of interest.


For a straight line graph, select any two points #(x_1,y_1)# and #(x_2,y_2)# on the line.
Calculate, #"Gradient"=(y_2-y_1)/(x_2-x_1)#
Recall that for an equation of line in the form #y=mx+c#,
#m# is the gradient or the slope of the line.
Gradient or slope could be positive or negative as shown in the straight line graphs above. Observe the value of #m#.

For curved graphs, one has to draw a tangent at the point of interest. Gradient of the tangent is the gradient of the graph at that point.

This is done by first drawing a line at 90 degrees to the curve at the point where one is required to calculate the gradient of curved graph, a normal or ⊥ line. Then drawing the tangent at 90 degrees to this normal.