For a set of data, the equation of the line of best fit is \(y=-3x+40\). (a) Use the equation to estimate the value of \(y\) when \(x=6\). [1] (b) Use the e...
Question 1 Report
For a set of data, the equation of the line of best fit is \(y=-3x+40\).
(a) Use the equation to estimate the value of \(y\) when \(x=6\). [1]
(b) Use the equation to estimate the value of \(x\) when \(y=10\). [2]
Answer Details
The line of best fit summarises the trend in the data, so its equation lets one variable be predicted from the other. Substituting a known value into the equation is all that is required.
(a) Put \(x=6\) into \(y=-3x+40\):
\(y=-3(6)+40=-18+40=22\) [B1] cao
(b) Here \(y\) is known and \(x\) is wanted, so form an equation and solve it:
- \(10=-3x+40\) [M1] oe
- \(3x=40-10=30\)
- \(x=10\) [A1] cao
The negative gradient of \(-3\) means \(y\) falls by \(3\) for every increase of \(1\) in \(x\), which is negative correlation. Be careful not to substitute \(10\) for \(x\) in part (b); the value given is a \(y\) value, and the two variables are not interchangeable.
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