Part of the curve \(y=\frac{8}{x}\) is drawn on the grid. Find the value of \(y\) when \(x=3.2\).
Question 1 Report
Part of the curve \(y=\frac{8}{x}\) is drawn on the grid.
Find the value of \(y\) when \(x=3.2\).
Answer Details
A point lies on the curve \(y = \frac{8}{x}\) exactly when its coordinates satisfy that equation, so the value of \(y\) at \(x = 3.2\) can be calculated directly rather than read off the grid. Calculating is more accurate than reading, since a graph can usually only be read to about half a small square.
\[ y = \frac{8}{3.2} = 2.5 \] [B1]If the division is not obvious, clear the decimal by multiplying top and bottom by \(10\): \(\frac{8}{3.2} = \frac{80}{32} = \frac{5}{2} = 2.5\).
This is a reciprocal (inverse proportion) curve: as \(x\) increases, \(y\) decreases, and their product is always \(8\). Check the answer with that property: \(3.2 \times 2.5 = 8\). The common error is to multiply instead of divide, giving \(25.6\), which fails the product check immediately.
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