Question

22.
The pair of points is on the graph of an inverse variation. Find the missing value.

(2.4, 3) and (5, y)

Answer 1

In an inverse variation, the product of the two variables is constant. This means if we have two pairs of points \((x_1, y_1)\) and \((x_2, y_2)\) that satisfy \(xy = k\), where \(k\) is a constant, we can find the missing value.

Given the points \((2.4, 3)\) and \((5, y)\):

1. First, we can find the constant \(k\) using the first point:
\[
k = x_1 \cdot y_1 = 2.4 \cdot 3 = 7.2
\]

2. Next, we can use this value of \(k\) to find \(y\) using the second point:
\[
k = x_2 \cdot y_2 \implies 7.2 = 5 \cdot y
\]

3. Now, solve for \(y\):
\[
y = \frac{7.2}{5} = 1.44
\]

Thus, the missing value \(y\) is \(1.44\).