smc-792-25-Sketch Line

Functions, 2ADV F1 2009 HSC 1a (Adapted)

Sketch the graph of \(y+\dfrac{x}{3} = 2\), showing the intercepts on both axes. (2 marks)

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\(y+\dfrac{x}{3} = 2\ \ \Rightarrow\ \ y=-\dfrac{1}{3}x+2\)

\(y\text{-intercept}\ = 2\)

\(\text{Find}\ x\ \text{when}\ y=0:\)

\(\dfrac{x}{3}=2\ \ \Rightarrow\ \ x=6\)

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`

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?

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`B`

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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)}`

`text(When)\ \ x = 1,\ y = 4`

`=>B`

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`

`ytext{-intercept}\ = 3`

`text{Find}\ x\ text{when}\ y=0:`

`0-2x=3\ \ =>\ \ x=-3/2`