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Which one of the following statements is not true?
A. The line with equation `7x - 4y = 0` passes through the point `(4, 7)`.
B. The point `(3, 5)` lies in the region defined by `7x - 4y >= 0`.
C. The line with equation `3x + 5y = 0` has a positive gradient.
D. The lines `7x - 4y = 0` and `3x + 5y = 0` meet at the origin.
E. For the line with the equation `7x - 4y = 0`, `y` increases as `x` increases.
`C`
`text(Consider)\ A`
`text(Sub)\ (4, 7)\ text(into)\ 7x − 4y = 0`
| `text(LHS)` | `= 7(4) − 4(7)` |
| `= 28 − 28` | |
| `= 0` | |
| `= text(RHS)` |
`:. text(True, eliminate)\ A.`
`text(Consider)\ B`
`text(Sub)\ (3, 5)\ text(into)\ 7x − 4y >= 0`
| `text(LHS)` | `= 7(3) − 4(5)` |
| `= 21 − 20` | |
| `= 1` | |
| `>= 0` |
`:. text(True, eliminate)\ B.`
`text(Consider)\ C`
| `3x + 5y` | `= 0` |
| `5y` | `= text(−3)x` |
| `y` | `= −3/5x` |
| `:.\ text(gradient)` | `= −3/5` |
| `= text(negative)` |
`:.\ text(False)`
`text(Similarly)\ D, E\ text(can be eliminated.)`
`=> C`