smc-6214-08-Intercepts

Functions, 2ADV 2011 HSC 3c

The diagram shows a line `l_1`, with equation `3x + 4y-12 = 0`, which intersects the `y`-axis at `B`.

A second line `l_2`, with equation `4x-3y = 0`, passes through the origin `O` and intersects `l_1` at `E`.

Show that the coordinates of `B` are `(0, 3)`. (1 mark)
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Show that `l_1` is perpendicular to `l_2`. (2 marks)
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a. `\text{See Worked Solution}`

b. `\text{See Worked Solution}`

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a. `B\ text(is)\ y text(-intercept of)\ l_1`

`text(When)\ x = 0:`

`(3 xx 0) + 4y-12=0\ \ =>\ \ y=3`

`:.\ B\ text(is)\ (0,3)`

`m(l_1)=-3/4`

`m(l_2)=4/3`

`m (l_1) xx m (l_2)= -3/4 xx 4/3= -1`

`:.\ l_1\ text(and)\ l_2\ text(are perpendicular)`

Which of the following could be the graph of `y= -2 x+2`?

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`A`

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`text{By elimination:}`

`y text{-intercept = 2 (Eliminate B and C)}`

`text{Gradient is negative (Eliminate D)}`

`=>A`

What is the `x`-intercept of the line `x + 3y + 6 = 0`?

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`A`

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`x text(-intercept occurs when)\ y = 0:`

`x + 0 + 6`	`= 0`
`x`	`= -6`

`:. x text{-intercept is}\ (-6, 0)`

`=> A`

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`