a. The constant of proportionality is k = 2
b. If Micah saves $150, his parents will give him $300
From mathematics, we know that [tex]y[/tex] varies directly as [tex]x[/tex] or [tex]y[/tex] is directly proportional to [tex]x[/tex] if and only if:
[tex]y=kx[/tex] for some nonzero constant [tex]k[/tex].
Here we know some facts:
In other words:
Let y be the money his parents give him.
Let x be the money that Micah saves.
[tex]We \ know \ that: \\ y=kx \\ \\ \\ Solving \ for \ k: \\ \\ k=\frac{y}{x} \\ \\ k=\frac{10}{5} \\ \\ \boxed{k=2}[/tex]
So, the constant of proportionality is k = 2
In this case, we know that Micah saves $150. So we need to find the amount of his parents will give him. So what we know here is the value of x, because x represents the amount of money Micah saves. Therefore, by knowing x and k, we can calculate the value of y, which is the amount of money his parents will give him. Hence:
[tex]For \ x=150 \ and \ k=2: \\ \\ y=2(150) \\ \\ \boxed{y=300}[/tex]
Finally, if Micah saves $150, his parents will give him 300$
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