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Algebra, STD2 A2 2012 HSC 5 MC (Adapted)

The line below has intercepts  \(m\)  and  \(n\),  where  \(m\) and  \(n\) are positive integers. 
  

What is the gradient of the line? 

  1. \(\dfrac{m}{n}\)
  2. \(\dfrac{n}{m}\)
  3. \(-\dfrac{m}{n}\)  
  4. \(-\dfrac{n}{m}\)
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\(C\)

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♦ Mean mark 45%
\(\text{Gradient}\) \(=\dfrac{\text{rise}}{\text{run}}\)
  \(=-\dfrac{m}{n}\)

\(\Rightarrow C\)

Algebra, STD2 A2 2004 HSC 2 MC (Adapted)

Michael drew a graph of the height of a plant.
  

What is the gradient of the line?

  1. 1
  2. 3
  3. 4.5
  4. 6
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\(B\)

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\(\text{2 points on graph}\ \ (0, 6),\ (1, 9)\)

\(\text{Gradient}\) \(=\dfrac{y_2-y_1}{x_2-x_1}\)
  \(=\dfrac{9-6}{1-0}\)
  \(=3\)

\(\Rightarrow B\)

Algebra, STD2 A2 2016 HSC 14 MC (Adapted)

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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\(B\)

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\(y\text{-intercept}\ (c)\ \text{is positive}\)

\(\rightarrow\ \text{eliminate A and D}\)

\(\text{gradient}\ (m)\ \text{is negative}\)

\(\rightarrow\ \text{eliminate C}\)

\(\Rightarrow B\)

Algebra, STD2 EO-Bank 2 MC

What is the gradient of the line  \(5x+7y+3=0\)?

  1. \(-\dfrac{7}{5}\)
  2. \(-\dfrac{5}{7}\)
  3. \(\dfrac{7}{5}\)
  4. \(\dfrac{5}{7}\)
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\(B\)

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\(5x+7y+3\) \(=0\)
\(7y\) \(=-5x-3\)
\(y\) \(=-\dfrac{5}{7}x-\dfrac{3}{7}\)

  
\(\therefore\ \text{Gradient}=-\dfrac{5}{7}\)

\(\Rightarrow B\)

Algebra, STD2 EO-Bank 11 MC

Petra drew a straight line through the points \((0, 4)\) and \((5, -3)\) as shown in the diagram below.
 

What is the gradient of the line that Petra drew?

  1. \(-\dfrac{7}{5}\)
  2. \(-\dfrac{5}{7}\)
  3. \(\dfrac{7}{5}\)
  4. \(\dfrac{5}{7}\)
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\(A\)

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\(\text{Line passes through } (0, 4)\ \text{and } (5, -3)\)

\(\text{Gradient}\) \(=\dfrac{y_2-y_1}{x_2-x_1}\)
  \(=\dfrac{4- -3}{0-5}\)
  \(=-\dfrac{7}{5}\)

 
\(\Rightarrow A\)