Question

Part A: Billy rented a canoe at $14 for 2 hours. If he rents the same canoe for 5 hours, he has to pay a total rent of $29. Write an equation in the standard form to represent the total rent (y) that Billy has to pay for renting the canoe for x hours. (4 points) Part B: Write the equation obtained in Part A using function notation. (2 points) Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points) Part A: Ax By= C

Answer 1

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 :)