Straight lines: gradient, parallel and perpendicular Problem set B Answers

1. (a) gradient \(-\frac{3}{4}\), y-intercept \(6\)
2. (b) \(x = 8\)
3. (c) \(y = -\frac{3}{4}x + 6\)

\(3x - 4y + 20 = 0\)

1. (a) parallel
2. (b) perpendicular
3. (c) neither

1. (a) \(k = -\frac{15}{2}\) (−7.5)
2. (b) \(k = \frac{6}{5}\) (1.2)

1. (a) Both gradients equal \(\frac{3}{2}\)
2. (b) \(t = 18\)

1. (a) €35 per hour
2. (b) €30: the fixed charge
3. (c) €310
4. (d) 10 hours

1. (a) \(-\frac{1}{2}\)
2. (b) \(y = -\frac{1}{2}x + \frac{23}{2}\)
3. (c) \((0, \frac{23}{2})\)

1. (a) PQ: \(\frac{3}{4}\); QR: \(-\frac{4}{3}\)
2. (b) \(\frac{3}{4} \times (-\frac{4}{3}) = -1\)
3. (c) 25 square centimetres

1. (a) \(m_1 = -\frac{k+2}{3}\), \(m_2 = -\frac{4}{k-1}\)
2. (b) k = 3.27 or k = −4.27
3. (c) \(k = -\frac57\)

1. (a) AB: \(-\frac{1}{5}\); BC: \(1\)
2. (b) \(x - y + 2 = 0\); \(x + 5y - 22 = 0\)
3. (c) \((2, 4)\)