(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 \(\frac{a}{b}\)
(a) A(-2, 7), B(2, -3)
m = \(\frac{y_2 - y_1}{x_2 - x_1} = \frac{-3 - 7}{2 - (-2)} = \frac{10}{4}\)
\(\frac{-5}{2} = \frac{y - 7}{x + 2}\)
-5(x + 3) = 2(y - 7)
-5x - 10 = 2y - 14
2y - 14 + 10 + 5x = 0
2y - 14 + 10 + 5x = 0
2y + 5x - 4 = 0
(b) \(\frac{5b - a}{8b + 3a} = \frac{1}{5}\)
5(5b - a) = 1(1)(8b + 3a)
25b - 5a = 8b + 3a
25b - 8b = 3a + 5a
17b = 8a
\(\frac{a}{b} = \frac{17}{8}\)
\(\frac{a}{b}\) = 2.13 to 2 d.p
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