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FM Intercepts

1.4 Analysing Non-Linear Graphs

Intercepts of Non-Linear Graphs

  • Non-linear graphs can have no intercepts, one intercept or multiple intercepts along either axis.

Example

Picture 2

Above is a graph showing the profits earned by a community theatre in the years before they changed management. In the context of this situation, we can say that the intercepts at t=-3, -2 and 1 years represent points at which the community theatre just broke even (i.e. no profit or loss). The intercept at P=$1000 represents the profits made in the year the new management took over.

Maximum/Minimum Points

  • It may interest us to know the highest, or lowest values that the y-variable has taken. For example, if we want to find the highest a tide has been in a year in order to know how high to build a support structure.
  • The maximum and minimum points of non-linear graphs will be points of 0 gradient or the endpoints of a section (i.e. where a graph ends or undergoes structural change).
  • There may be multiple minimum points and/or multiple maximum points.
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1.1 Straight Line Graphs

Straight Line Graphs

  • Relationships of the form: y=mx+c, where m is the gradient and c is the y-intercept, can be modelled graphically as a straight line.

Example

Picture 1

Above is the graph for the linear relationship: y=-2x+1

Intercepts

  • Two points which are often of interest in graphs are the points at which they cross the x-axis, and where they cross the y-axis. These are known as the x-intercept and y-intercept, respectively.
  • To find the x-intercept given a formula, set y to 0 and solve for x.
  • To find the y-intercept given a formula, set x to 0 and solve for y.
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