2 : 3 = .... : 9 ? 5 : 10 = 20 : ...? 1 : 3 = 8 : 24 ......? 4 : 3 = 16 : 2 ....?
2 answers:
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<em>It's nice of you to offer, but no thanks.</em>
To correctly graph this, you need to set up a simple equation and table of values. Luckily, this equation is dead-simple; I'll define <em>y</em> as the total cost and <em>x</em> as the number of water bottles sold.
Since 1.50$ is the cost for one bottle, multiplying that with your variable that defined the amount of bottles, <em>x</em>, gets you the total, <em>y</em>. Now that we have a basic equation, we can begin plugging in values.
Recall that a function is basically just something that takes in a value and returns another one; in our case, it takes the <em>amount of bottles</em> and returns the <em>total cost. </em>Now, plug in the x-values present on the graph (specifically only whole numbers, since you can't have a half bottle). I can't make a proper table but I'll make do.
x y
--------
0 0
1 1.5
2 3
3 4.5
4 6
5 7.5
-----------
Great, now that you have a table of values all you have to do is plug them into the graph, which I've attached. It's pretty crude since I drew it in mspaint but I'm sure you get the point at this point.
Substitute this into the parabolic equation,
We're told the line intersects
twice, which means the quadratic above has two distinct real solutions. Its discriminant must then be positive, so we know
We can tell from the quadratic equation that has its vertex at the point (3, 6). Also, note that
and
so the furthest to the right that extends is the point (5, 2). The line
passes through this point for
. For any value of
, the line
passes through
either only once, or not at all.
So ; in set notation,