Calculus&Mathematica: Example 1

Example Solution

Producer: Bruce Carpenter

Publisher: Math Everywhere, Inc. Distributor: Wolfram Research, Inc.

EXAMPLE
SOLUTION

G.1) Line fundamentals*

G.1.e)

Here are two points {1,3} and {3,2}:


     point1 = Graphics[{Blue, PointSize[0.03],
       Point[{1,3}]}];
     point2 = Graphics[{Blue,PointSize[0.03],
       Point[{3,2}]}];

     twopoints = 
     Show[point1, point2, PlotRange->{{0,5},{0,5}},
       AxesOrigin->{0,0}, Axes-&gtTrue, AxesLabel->{"x","y"},
       AspectRatio-&gtAutomatic];

Find a formula for the line function whose plot hits both points.

Confirm your answer with a plot.

My function will be called House and its variable will be dog. It is supposed to be a line...


     Clear[House,dog,a,b]
     House[dog_] = a dog + b
     b + a dog

According to these points, when dog = 1, House should equal 3, and when dog = 3, House should = 2.

     House[1]
     a + b

That should equal 3

     House[3]
     3 a + b

That should equal 2

I need to find a and b that will make these equal what they are supposed to.

     Solve[{a + b == 3, 3 a + b == 2},{a,b}]
    
     a = -1/2
     b = 7/2
         -1/2
          7/2

Here's the function...

     House[dog]
     7/2 - dog/2

If I plot this function, it should go through those two points. Let's see...

     myfunction = Plot[House[x], {x,0,5}]

     Show[twopoints,myfunction]

I say, I am correct. What do you say?

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