Functions & Linear Graphs
Shinglee Think Mathematics 1A — Chapter 6 (Sec 1)
Prepared by Miss Clarissa Ng
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Q1. Find the gradient and the y-intercept of each line:
(a) y = 3x + 5
(b) y = −12x − 4
(c) 3y + 6x = 9
(d) 5x − 2y = 10
Q2. Write each equation in the form y = mx + c, then state its gradient and y-intercept:
(a) 4x − 3y = 12
(b) 6x + 2y = 8
Q3. Find the gradient of the line passing through each pair of points:
(a) (1, 2) and (3, 8)
(b) (−2, 5) and (4, −7)
Q4. State whether each pair of lines is parallel, perpendicular or neither:
(a) y = 3x + 1 and y = 3x − 7
(b) y = 5x + 2 and y = −15x + 4
(c) 2y = x + 6 and y = 2x − 3
Q5. Which of the following lines passes through the point (2, −1)? Show your working:
(a) y = 3x − 7
(b) y = x − 3
(c) y = −2x + 5
Q1. Find the equation of the line passing through each pair of points. Give your answer in the form y = mx + c:
(a) (2, 5) and (4, 11)
(b) (−3, −1) and (1, 7)
Q2. The line L1 has equation y = 4x + 1. Find the equation of the line which is parallel to L1 and passes through (3, 2). Give your answer in the form y = mx + c.
Q3. The line L1 has equation y = 4x + 1. Find the equation of the line which is perpendicular to L1 and passes through (0, 5). Give your answer in the form y = mx + c.
Q4. Find the equation of each line. Give your answer in the form y = mx + c:
(a) passes through (1, 4) and is parallel to the line y = −2x + 5
(b) passes through (−2, 4) and is perpendicular to the line 3y = x + 9
Q5. The line L2 passes through (0, −3) and is parallel to the line 4x + 2y = 10. Find the equation of L2.
Q6. The line L3 passes through (2, −1) and is perpendicular to the line y = −14x + 6. Find the equation of L3.
Q1. The cost, C dollars, of a taxi ride for d kilometres is given by the equation C = 2.5d + 4.
(a) Find the cost of a 6 km ride.
(b) What does the value 4 represent in this context?
Q2. The table shows the cost, C dollars, of a taxi ride for d kilometres.
| d (km) | C ($) |
|---|---|
| 2 | 9 |
| 5 | 18 |
(a) Find the equation of C in terms of d.
(b) How much would a 10 km ride cost?
Q3. In the figure, ABCD is a rectangle with A(1, 2), B(3, 4) and C(6, 1). Find the equation of the line passing through D and C. Give your answer in the form y = mx + c.
Q4. (OPEN) The line y = kx + 2 is perpendicular to the line y = −3x + 7. Find the value of k.
| Q1(a) | m = 3, c = 5 |
| Q1(b) | m = −½, c = −4 |
| Q1(c) | y = −2x + 3 → m = −2, c = 3 |
| Q1(d) | y = (5/2)x − 5 → m = 5/2, c = −5 |
| Q2(a) | y = (4/3)x − 4 → m = 4/3, c = −4 |
| Q2(b) | y = −3x + 4 → m = −3, c = 4 |
| Q3(a) | m = (8−2)/(3−1) = 3 |
| Q3(b) | m = (−7−5)/(4+2) = −2 |
| Q4(a) | Parallel (both m = 3) |
| Q4(b) | Perpendicular (m₁ × m₂ = 5 × (−1/5) = −1) |
| Q4(c) | Neither (m = ½ and m = 2; not equal, product ≠ −1) |
| Q5 | (a) y = 3x − 7 — substituting x = 2 gives y = −1 ✓ |
| Q1(a) | m = (11−5)/(4−2) = 3; y − 5 = 3(x − 2) → y = 3x − 1 |
| Q1(b) | m = (7+1)/(1+3) = 2; y − 7 = 2(x − 1) → y = 2x + 5 |
| Q2 | y = 4x − 10 (parallel: m = 4; through (3, 2): c = 2 − 12) |
| Q3 | y = −(1/4)x + 5 (perpendicular: m = −1/4; passes through (0, 5) so c = 5) |
| Q4(a) | y = −2x + 6 (parallel keeps m = −2; c = 4 + 2(1)) |
| Q4(b) | y = −3x − 2 (perpendicular to m = 1/3 → m = −3; c = 4 − 6) |
| Q5 | y = −2x − 3 (parallel to m = −2; through (0, −3) so c = −3) |
| Q6 | y = 4x − 9 (perpendicular to m = −1/4 → m = 4; c = −1 − 8) |
| Q1(a) | C = 2.5(6) + 4 = $19 |
| Q1(b) | The fixed starting fare (cost when d = 0) |
| Q2(a) | m = (18−9)/(5−2) = 3; C − 9 = 3(d − 2) → C = 3d + 3 |
| Q2(b) | C = 3(10) + 3 = $33 |
| Q3 | D(4, 3); m = (1−3)/(6−4) = −1 → y = −x + 7 |
| Q4 | k × (−3) = −1 → k = ⅓ |