(a) Find the equation of the line which passes through the points A(-2, 7) and B(2, -3) (b) Given that \(\frac{5b - a}{8b + 3a} = \frac{1}{5}\) = find, corr...
Question 1 Report
(a) Find the equation of the line which passes through the points A(-2, 7) and B(2, -3)
(b) Given that \(\frac{5b - a}{8b + 3a} = \frac{1}{5}\) = find, correct to two decimal places, the value \(\frac{a}{b}\)
Answer Details
(a) Equation of the line through \(A(-2,7)\) and \(B(2,-3)\).
Gradient \(m=\dfrac{-3-7}{2-(-2)}=\dfrac{-10}{4}=-\dfrac{5}{2}\).
\(y-7=-\dfrac{5}{2}(x+2)\Rightarrow y=-\dfrac{5}{2}x-5+7=-\dfrac{5}{2}x+2\).
\(y=-\dfrac{5}{2}x+2\), i.e. \(5x+2y-4=0\).
(b) \(\dfrac{5b-a}{8b+3a}=\dfrac{1}{5}\).
Cross-multiply: \(5(5b-a)=8b+3a \Rightarrow 25b-5a=8b+3a\).
\(25b-8b=3a+5a \Rightarrow 17b=8a \Rightarrow \dfrac{a}{b}=\dfrac{17}{8}=2.125\).
\(\dfrac{a}{b}\approx 2.13\) (2 d.p.).
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