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

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

\(2x + 5y + 5 = 0\)

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

1. (a) \(k = -\frac{8}{3}\) (−2.67)
2. (b) \(k = 6\)

1. (a) Both gradients equal \(2\)
2. (b) \(t = 15\)

1. (a) €25 per month
2. (b) €40: the fixed charge
3. (c) €390
4. (d) 13 months

1. (a) \(\frac{1}{2}\)
2. (b) \(y = \frac{1}{2}x + 8\)
3. (c) \((0, 8)\)

1. (a) PQ: \(\frac{1}{2}\); QR: \(-2\)
2. (b) \(\frac{1}{2} \times (-2) = -1\)
3. (c) 5 square metres

1. (a) \(m_1 = -\frac{k+1}{2}\), \(m_2 = -\frac{3}{k-2}\)
2. (b) k = 3.37 or k = −2.37
3. (c) \(k = \frac15\)

1. (a) AB: \(\frac{2}{5}\); BC: \(\frac{5}{3}\)
2. (b) \(5x - 3y - 2 = 0\); \(2x - 5y + 22 = 0\)
3. (c) \((4, 6)\)