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?
- `(0, 6)`
- `(1, 4)`
- `(2, 2)`
- `(3, 0)`
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`text(Method 1 – Graphically)`
`text(From graph, intersection at)\ (1,4)`
`=>B`
`text(Method 2 – Algebraically)`
| `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`