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v2 Functions, 2ADV F1 2017 HSC 1 MC

What is the gradient of the line  \(6x+7y-1 = 0\)?

  1. \(-\dfrac{6}{7}\)
  2. \(\dfrac{6}{7}\)
  3. \(-\dfrac{7}{6}\)
  4. \(\dfrac{7}{6}\)
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\(A\)

Show Worked Solution
\(6x+7y-1\) \(=0\)  
\(7y\) \(=-6x+1\)  
\(y\) \(=-\dfrac{6}{7}x+\dfrac{1}{7}\)  

 
\(\Rightarrow A\)

v1 Functions, 2ADV F1 2017 HSC 1 MC

What is the gradient of the line \(4x-5y-2 = 0\)?

  1. \(-\dfrac{4}{5}\)
  2. \(\dfrac{4}{5}\)
  3. \(\dfrac{5}{4}\)
  4. \(-\dfrac{5}{4}\)
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\(B\)

Show Worked Solution
\(4x-5y-2\) \(=0\)  
\(-5y\) \(=-4x + 2\)  
\(y\) \(=\dfrac{4}{5}x-\dfrac{2}{5}\)  

 
\(\Rightarrow B\)

Algebra, STD2 A2 SM-Bank 10 MC

Leo drew a straight line through the points (0, 5) and (3, -2) as shown in the diagram below.
 

 
What is the gradient of the line that Leo drew?

  1. `7/3`
  2. `3/7`
  3. `-3/7`
  4. `-7/3`
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`D`

Show Worked Solution

`text{Line passes through (0, 5) and (3, – 2)}`

`text(Gradient)` `= (y_2-y_1)/(x_2-x_1)`
  `= (5-(-2))/(0-3)`
  `= -7/3`

 
`=>D`

Algebra, STD2 A2 SM-Bank 2 MC

What is the gradient of the line  `2x + 3y + 4 = 0`?

  1.   `-2/3`
  2. `2/3`
  3.   `-3/2`
  4.   `3/2`
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`A`

Show Worked Solution
`2x + 3y + 4` `= 0`
`3y` `= -2x – 4`
`y` `= -2/3 x – 4/3`
`:.\ text(Gradient)` `= -2/3`

`=>  A`

Functions, 2ADV F1 2017 HSC 1 MC

What is the gradient of the line  `2x + 3y + 4 = 0`?

  1. `-2/3`
  2. `2/3`
  3. `-3/2`
  4. `3/2`
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`A`

Show Worked Solution
`2x + 3y + 4` `= 0`
`3y` `= -2x-4`
`y` `= -2/3 x-4/3`
`:.\ text(Gradient)` `= -2/3`

 
`=>  A`

Functions, 2ADV F1 2015 HSC 2 MC

What is the slope of the line with equation  `2x - 4y + 3 = 0`?

  1. `-2`
  2. `-1/2`
  3. `1/2`
  4. `2`
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`C`

Show Worked Solution
`2x – 4y + 3` `= 0`
`4y` `= 2x + 3`
`y` `= 1/2 x + 3/4`

`:.\ text(Slope)\ = 1/2`

`=> C`

Algebra, STD2 A2 2004 HSC 2 MC

Susan drew a graph of the height of a plant.
  

What is the gradient of the line?

  1. `1`
  2. `5`
  3. `7.5`
  4. `10`
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`B`

Show Worked Solution

`text(2 points on graph)\ \ (0, 10),\ (1, 15)`

`text(Gradient)` `= (y_2-y_1) / (x_2-x_1)`
  `= (15-10) / (1-0)`
  `= 5`

`=> B`

Algebra, STD2 A2 2012 HSC 5 MC

The line  `l`  has intercepts  `p`  and  `q`,  where  `p`  and  `q`  are positive integers. 
  

What is the gradient of line  `l ` ? 

  1. `-p/q`  
  2. `-q/p`  
  3. `\ \ \ p/q`  
  4. `\ \ \ q/p`  
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`A`

Show Worked Solution
 
♦ Mean mark 45%
`text(Gradient)` `= text(rise)/text(run)`
  `= -p/q`

`=>  A`