Is the relationship shown by the data linear?If it is,model the data with an equation?a.(2,6)(3,4)(4,2)(5,0) b.(-2,-7)(-1,-4)(1,2)(3,8) c:(-3,0)(-1,3)(1,7)(3,9)

Question

A little rusty with the math. School just started back and I need to refresh my memory. Any help would be appreciated.

Answer 1

Here is a tedious way to answer the question:

 

In a particular set of points, pick any 2 points in the set, find the slope m, and then use one of the two points to get the equation of a line in the form

 

y = mx + b.

 

Then test to see if the other points in the set obey this equation.  If they do, the relationship is linear.  Do this for all three sets of points.

 

Here is a graphical way to answer the question:

 

For a particular set of points, plot the points of each set in the Cartesian plane, and see if they fall on the same straight line.  Visualization may be the fastest way to see if a relation is linear or not.  Personally, I prefer visualization.  But your assignment might require you to do the calculations as in the tedious method above.

 

There is also the matter of how close to a perfectly straight line you need to be, in case the points come close to aligning in a straight line, but do not exactly match a straight line.  But that gets into curve fitting, which is another subject.