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Cartesian Plane, SMB-011

Rambo drew a line as shown on the grid below.

What is the gradient of Rambo's line?  (3 marks)

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`-7/5`

Show Worked Solution

`text{Line goes through}\ (-3,4) and (2,-3).`

`text(Using the gradient formula):`

`m` `=(y_2-y_1)/(x_2-x_1)`  
  `=(-3-4)/(2-(-3))`  
  `=-7/5`  

Linear Relationships, SMB-001 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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`-7/3`

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`

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`

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?

  1. `m` is positive and `c` is negative
  2. `m` is negative and `c` is positive
  3. `m` and `c` are both positive
  4. `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 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`