(a) (i) Using a scale of 2 cm to 1 unit on both axes, on the same graph sheet, draw the graphs of (y – frac{3x}{4} = 3) and (y + 2x = 6).
(ii) From your graph, find the coordinates of the point of intersection of the two graphs.
(iii) Show, on the graph sheet, the region satisfied by the inequality (y – frac{3}{4}x geq 3).
(b) Given that (x^{2} + bx + 18) is factorized as ((x + 2)(x + c)). Find the values of c and b.
Explanation
(a)(i) R is the required region.
(iii) Coordinates of the point of intersection of the two graphs = (1.1, 3.8)
(b) Assuming (y – frac{3x}{4} = 3)
If x = 0, (y – frac{3}{4}(0) = 3 implies y = 3)
If y = 0, (0 – frac{3}{4}x = 3 implies -3x = 12 ; x = – 4)
| x | 0 | -4 |
| y | 3 | 0 |
Assuming (y + 2x = 6)
If x = 0, (y + 2(0) = 6 implies y = 6)
If y = 0, (0 + 2x = 6 implies 2x = 6 ; x = 3)
| x | 0 | 3 |
| y | 6 | 0 |
(b) ((x + 2)(x + c) = x^{2} + 2x + cx + 2c)
(x^{2} + (2 + c)x + 2c = x^{2} + bx + 18)
( 2c = 18 ; c = 9)
(b = 2 + c = 2 + 9 = 11)
(b, c) = (11, 9).