Part A)
So we need the graph to pass through these points:
time = 2 and price=$14 -> (2,14)
time= 5 and price = $29 -> (5,29)
Standard form:
Ax+By = C
Let’s replace the points:
A*2+B*14=C
A*5+B*29=C
Let’s eliminate variables:
(A*2+B*14)-(A*5+B*29)=C-C
A*2+B*14-A*5-B*29=0
-3A-15B=0
-3A=15B
A=15B/-3
A=-5B
There are several numbers that verify this proportion. For
example, if B=1, A=-5 (you can try others, there is not only 1 correct answer).
So we can make this equation:
-5x+y=C
Then we can calculate C using one point:
-5*2+14=C
-10+14=C
4=C
So one of the possible equations is: -5x+y=4
(Remember there are multiple correct answers for this
item)
You can verify it with the other point:
-5*5+29=-25+29=4 ->OK
Part B)
Whatever you have found in Part A, you will find the same in
Part B when you convert it to function notation. All you have to do is clear y:
-5x+y=4
y=4+5x
So the equation is: f(x)=4+5x
Part C)
First of all, you have to find f(0)
f(x)=4+5x
f(0) =4+5*0=4+0=0
f(0) is ALWAYS the constant not multiplied by x.
So you know it has to cross the y axes in y=4
Now let’s put 0 as y-value:
4+5x=0
5x=0-4=-4
x=-4/5
So now you know it has to cross the x axes in x=-4/5.
So you can put those intersections in the graph and you draw
the line through those points. Labels: horizontal axes is x, and in this case represents time; vertical axes is y, and in this case represents price.
Remember there are other methods, too :)
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