Sketch the graph of `y - 2x = 3`, showing the intercepts on both axes. (2 marks)
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`y-2x=3\ \ => \ \ y=2x+3`
Algebra, STD2 A4 2017 HSC 17 MC
The graph of the line with equation `y = 6 - 2x` is shown.
When the graph of the line with equation `y = x + 3` is also drawn on this number plane, what will be the point of intersection of the two lines?
A. `(0, 6)`
B. `(1, 4)`
C. `(2, 2)`
D. `(3, 0)`
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`text(Solution 1)`
`text(From graph, intersection at (1,4))`
`=>B`
`text(Solution 2)`
| `y` | `= 6 – 2x` | `…\ (1)` |
| `y` | `= x + 3` | `…\ (2)` |
`text{Substitute (2) into (1)}`
| `x + 3` | `= 6 – 2x` |
| `3x` | `= 3` |
| `x` | `= 1` |
`text(When)\ \ x = 1, y = 4`
`=>B`