1. 1
   A delivery company models the cost of three delivery routes as straight-line graphs. Route 1 has equation $y=4x-7$. Route 2 passes through the points $(2,5)$ and $(6,17)$. Route 3 is parallel to $y=3x+1$ and passes through $(0,4)$.

   (a)

   A straight line has equation $y=4x-7$. What is its gradient?

   [1 mark]

   • A$4$
   • B$-7$
   • C$7$
   • D$-4$

   (b)

   Route 2 passes through the points $(2,5)$ and $(6,17)$. What is the gradient of this line?

   [1 mark]

   • A$2$
   • B$4$
   • C$3$
   • D$6$

   (c)

   Route 3 is parallel to $y=3x+1$ and passes through $(0,4)$. What is the equation of Route 3?

   [1 mark]

   • A$y=3x+1$
   • B$y=3x+4$
   • C$y=4x+3$
   • D$y=-3x+4$

   Total for question 1: 3 marks

2. 2
   A phone company offers a contract with monthly cost $y=2x+15$, where $x$ is gigabytes of data used and $y$ is cost in dollars. A rival contract passes through the points $(3,21)$ and $(9,39)$.

   (a)

   A phone contract's monthly cost, $y$ dollars, for $x$ gigabytes of data used is given by $y=2x+15$. State the gradient and the $y$-intercept, and explain what each represents in this context.

   [2 marks]

   (b)

   A rival phone contract's cost graph passes through the points $(3,21)$ and $(9,39)$. Find the equation of this line in the form $y=mx+c$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Two straight lines are studied on a coordinate grid. Line $L_1$ passes through the points $(1,4)$ and $(4,13)$. Line $L_2$ is perpendicular to $L_1$ and passes through the point $(3,7)$.

   (a)

   Line $L_1$ passes through the points $(1,4)$ and $(4,13)$. Find the equation of $L_1$ in the form $y=mx+c$, showing your working clearly.

   [3 marks]

   (b)

   Line $L_2$ is perpendicular to $L_1$ and passes through the point $(3,7)$. Find the equation of $L_2$ in the form $y=mx+c$.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A construction firm plans a straight access road through points $A(2,3)$ and $B(8,15)$ on a site plan (coordinates in hundreds of metres). A second road must be built parallel to $AB$, passing through point $C(0,6)$. A third road must be built perpendicular to $AB$, crossing it exactly at point $A$.

   (a)

   A construction firm plans a straight access road represented by the line through points $A(2,3)$ and $B(8,15)$ on a site plan, with coordinates in hundreds of metres. Find the equation of line $AB$ in the form $y=mx+c$, showing all working.

   [4 marks]

   (b)

   A second road is built parallel to $AB$, passing through point $C(0,6)$. Find the equation of this second road in the form $y=mx+c$.

   [4 marks]

   (c)

   A third road must be built perpendicular to $AB$, crossing it exactly at point $A(2,3)$. Find the equation of this third road in the form $y=mx+c$, showing all steps, and verify that point $A$ lies on your line.

   [5 marks]

   Total for question 4: 13 marks

End of questions