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v1 Algebra, STD2 A2 2012 HSC 5 MC

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%
\(\text{Gradient}\) \(=\dfrac{\text{rise}}{\text{run}}\)
  \(=-\dfrac{m}{n}\)

\(\Rightarrow C\)

v1 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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\(B\)

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

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

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

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

\(\Rightarrow B\)

v1 Algebra, STD2 A2 SM-Bank 10 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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\(\text{Line passes through } (0, 4)\ \text{and } (5, -3)\)

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

 
\(\Rightarrow A\)