Question

y varies inversely with twice the value of x. When y = 10, x = 3. Find y when x = 5.

Answer 1

inversely think divide

y=k/(2 x)

Answer 2

Y=K/X inverse, Y = KX direct

Answer 3

to find the constant of variation (k)
we use y = k/x
we know that y = 10 when x = 3
10 = k/3
10*3=k = 30
when x is 5, y is:
y = k/x
y = 30/5
y= 6

Answer 4

You need to put the first sentence into a line equation, form of y = mx + b. We know the slope is -2, as y goes down by 2 when x goes up by 1 (m = (change in y/change in x). So...

y = -2x + b

Now, let's solve for b by inputting your known coordinates, (3, 10)

10 = -2 * 3 + b

b = 16

So... now we know the full line equation:

y = -2x + 16

We can now substitute 5 in for x to find our y value.

y = -2(5) + 16

y = -10 + 16

y = 6

Answer 5

\[y=\frac{k}{2 x}\]
\[10=\frac{k}{2 \cdot 3} => 10=\frac{k}{6} => 60=k\]
\[y=\frac{60}{2 x}=\frac{30}{x}\]
\[y=\frac{30}{x}\]
\[y=\frac{30}{5}=6\]