1. 1
   A hiking trail's elevation changes linearly with horizontal distance along a straight section.

   (a)

   A hiking trail's elevation, $y$ metres, changes with horizontal distance, $x$ km, along a straight section passing through $(2, 100)$ and $(6, 180)$. Find the gradient of this section.

   [1 mark]

   • A20
   • B80
   • C0.05
   • D40

   (b)

   Using the gradient of 20 and the point $(2,100)$, find the value of $c$ in the equation $y = 20x + c$ for this trail section.

   [1 mark]

   • A$c = 100$
   • B$c = 140$
   • C$c = 60$
   • D$c = 20$

   (c)

   Using $y = 20x + 60$, find the elevation when the horizontal distance is $x = 10$ km.

   [1 mark]

   • A60
   • B200
   • C280
   • D260

   Total for question 1: 3 marks

2. 2
   A cable car track is modelled by a straight-line graph relating height to horizontal distance.

   (a)

   A cable car track can be modelled by a straight line passing through $(0, 50)$ and $(4, 130)$, where $x$ is horizontal distance in metres and $y$ is height in metres. Find the gradient of this line.

   [2 marks]

   (b)

   Using the gradient found in part (a) and the point $(0, 50)$, find the equation of the cable car line in the form $y = mx + c$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   An architect designs a ramp and a supporting rail using linear graphs, one of which must be parallel to the ramp.

   (a)

   An architect designs a ramp with a straight-line profile passing through $(1, 7)$ and $(4, 16)$, where $x$ is horizontal distance and $y$ is height, both in metres. Find the equation of the ramp in the form $y = mx + c$.

   [3 marks]

   (b)

   A supporting rail must run parallel to the ramp $y = 3x + 4$ and pass through the point $(2, 3)$. Find the equation of the supporting rail's line, in the form $y = mx + c$.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A telecoms engineer models two signal cables and a support strut using straight-line equations, including one perpendicular relationship.

   (a)

   A telecoms engineer models a signal cable as a straight line through $(-2, 1)$ and $(2, 9)$. Find the equation of this line in the form $y = mx + c$, then rewrite it in the form $ax + by = c$ with integer coefficients.

   [4 marks]

   (b)

   A second signal cable must be perpendicular to $y = 2x + 5$ and pass through the point $(4, 1)$. Find the equation of this second cable, in the form $y = mx + c$.

   [4 marks]

   (c)

   A support strut must be built along the perpendicular bisector of the line segment joining the two cable connection points $(-2, 1)$ and $(2, 9)$. Find the equation of the perpendicular bisector, showing all steps clearly.

   [5 marks]

   Total for question 4: 13 marks

End of questions