a) y = 9216
b) y = 360
Since x and y vary directly, y and x are directly related and can be expressed as y = kx. where k is a constant
y will increase as x increases. y will also decrease as x decreases.
I used k1 and k2 to separate the two questions and avoid confusion but using the constant k is fine.
a) For part a, you can substitute y = kx with the values of y and x.
[tex]1024 = k1 \times 9[/tex]
Hence, we can find the constant k1
[tex]k1 = \frac{1024}{9} [/tex]
Now, we can plug in the values into the original equation and obtain the new equation
[tex]y = \frac{1024}{9} x[/tex]
We can now solve part a by plugging in 81 into the value of x.
[tex]y = \frac{1024}{9} \times 81 = 9216[/tex]
b) Like part a, we can use the same method to find y for part b.
substitute y = kx with the values of y and x.
[tex]72 = k2 \times \frac{1}{2} [/tex]
Hence, we can find the constant k2
[tex]k2 = 72 \div \frac{1}{2} = 144[/tex]
Now, we can plug in the values into the original equation and obtain the new equation
[tex]y = 144x[/tex]
We can now solve part a by plugging in 5/2 into the value of x.
[tex]y = 144 \times \frac{5}{2} = 360[/tex]
