smc-792-20-Equation of Line

Algebra, STD2 A2 2024 HSC 2 MC

Consider the function shown.

Which of the following could be the equation of this function?

\(y=2 x+3\)
\(y=2 x-3\)
\(y=-2 x+3\)
\(y=-2 x-3\)

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\(C\)

Show Worked Solution

\(\text {Gradient is negative (top left } \rightarrow \text { bottom right)}\)

\(y \text{-intercept = 3 (only positive option)}\)

\(\Rightarrow C\)

Algebra, STD2 A2 2022 HSC 2 MC

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`

♦ Mean mark 48%.

Algebra, STD2 A2 SM-Bank 12 MC

Which of these equations represents the line in the graph?

`y = 11 - 2x`
`y = 11 + 5.5x`
`y = 11 - 5.5x`
`y = 11 + 2x`

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`A`

Show Worked Solution

`text{Graph passes through (0, 11) and (5.5, 0)}`

`text(Gradient)`	`=(y_2-y_1)/(x_2-x_1)`
	`=(11-0)/(0-5.5)`
	`=-2`

`:.\ text(Equation is:)\ \ y = 11 – 2x`

`=> A`

Algebra, STD2 A2 SM-Bank 11 MC

What is the equation for the line shown?

`y = -3/2 x + 2`
`y = 3/2 x + 2`
`y = -2/3 x + 2`
`y = 2/3 x + 2`

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`=>B`

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`text(Graph cuts)\ y text(-axis at 2)`

`text(Gradient) = text(rise)/text(run) = 3/2`

`:. y = 3/2 x + 2`

`=>B`

Algebra, STD2 A2 SM-Bank 5

The diagram shows the graph of a line.

What is the equation of this line? (2 marks)

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`y = 3/5x + 3`

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`ytext(-intercept = 3)`

`text(Gradient)`	`= text(rise)/text(run)`
	`= 3/5`

`:. text(Equation:)\ \ y = 3/5x + 3`

Functions, 2ADV F1 2018 HSC 3 MC

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

`(-6, 0)`
`(6, 0)`
`(0, -2)`
`(0, 2)`

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`A`

Show Worked Solution

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

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

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

`=> A`

Algebra, STD2 A2 SM-Bank 5 MC

The equation of the line drawn in the diagram below is:

`5y = 3x`
`y = 5/3x + 5`
`y = 3/5x + 5`
`y = -5/3x + 5`

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`D`

Show Worked Solution

`y text(-intercept) = +5`

`text(Gradient)`	`= text(rise)/text(run)`
	`=- 5/3`

`:.\ text(Equation is):\ y = -5/3x + 5`

`=> D`

Algebra, STD2 A2 2016 HSC 14 MC

The graph shows a line which has an equation in the form `y = mx + c`.

Which of the following statements is true?

`m` is positive and `c` is negative
`m` is negative and `c` is positive
`m` and `c` are both positive
`m` and `c` are both negative

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`=> A`

Show Worked Solution

`m` is the gradient and the line slopes to the right so `m` is positive.

`c` is the `y`-intercept which is negative.

`:.\ m` is positive and `c` is negative.

`=> A`

Algebra, STD2 A2 2015 HSC 13 MC

What is the equation of the line `l`?

`y = -2x + 2`
`y = 2x + 2`
`y = -x/2 + 2`
`y = x/2 +2`

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`A`

Show Worked Solution

`l\ text{passes through (0, 2) and (1, 0)}`

♦ Mean mark 48%.

`text(Gradient)`	`= (y_2-y_1)/(x_2-x_1)`
	`= (0-2)/(1-0)`
	`= -2`

`y\ text(intercept = 2)`

`:.y = -2x + 2`

`=>A`

Algebra, STD2 A2 2006 HSC 7 MC

Which equation represents the relationship between `x` and `y` in this table?

`y = 2x+1`
`y = 2x-2`
`y = x/2-2`
`y = x/2+1`

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`D`

Show Worked Solution

`text{By elimination (using the table)}`

`(0, 1)\ text(must satisfy)`

`:.\ text(NOT)\ B\ text(or)\ C`

`(2, 2)\ text(must satisfy)`

`:.\ text(NOT)\ A`

`=> D`

Algebra, STD2 A2 2014 HSC 7 MC

Which of the following is the graph of `y = 2x-2`?

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`D`

Show Worked Solution

♦ Mean mark 46%

`y = 2x-2`

`text(By elimination)`

`text(It has a)\ y\ text(intercept of)\ -2`

`=> text(Cannot be)\ B\ text(or)\ C`

`(-1, 0)text{ from}\ A\ text(doesn’t satisfy equation)`

`text(but)\ (1,0)\ text(from)\ D\ text(does)`

`=> D`