(a) Find the equation of the line which passes through the points A(-2, 7) and...

Explanation

(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