Equations of straight linesEdexcel A-Level Maths: Subtopic test

1. 1
   The line $l_1$ passes through the points $A(1,4)$ and $B(5,12)$.

   (a)

   Find the gradient of $l_1$.

   [1 mark]

   • A$\frac12$
   • B$2$
   • C$8$
   • D$4$

   (b)

   Find the equation of $l_1$.

   [1 mark]

   • A$y=2x+4$
   • B$y=2x-2$
   • C$y=\frac12x+\frac72$
   • D$y=2x+2$

   (c)

   Find an equation of the line through $C(6,0)$ that is perpendicular to $l_1$, giving your answer in the form $ax+by+c=0$, where $a$, $b$ and $c$ are integers.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The line $l$ has equation $3x-4y+12=0$.

   (a)

   Find the gradient of $l$.

   [1 mark]

   • A$\frac43$
   • B$-\frac34$
   • C$\frac34$
   • D$3$

   (b)

   Which of these lines is perpendicular to $l$?

   [1 mark]

   • A$4x+3y-7=0$
   • B$3x+4y+1=0$
   • C$4x-3y+2=0$
   • D$3x-4y-5=0$

   (c)

   The line $l$ meets the coordinate axes at the points $X$ and $Y$. Find the area of triangle $OXY$, where $O$ is the origin.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The points $P(-2,1)$, $Q(4,5)$ and $R(6,2)$ are the vertices of a triangle.

   (a)

   Show that $PQ$ is perpendicular to $QR$.

   [3 marks]

   (b)

   Find the exact area of triangle $PQR$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A taxi firm charges a fixed fee plus a constant rate per mile. A $4$-mile journey costs $\pounds11$ and a $10$-mile journey costs $\pounds20$. The charge $\pounds C$ for a journey of $d$ miles is modelled by a straight line.

   (a)

   (i) Find an equation for $C$ in terms of $d$.
   (ii) Interpret the gradient and the $C$-intercept of this line in the context of the taxi firm.

   [6 marks]

   (b)

   A rival firm charges a fixed fee of $\pounds8$ plus $\pounds1.20$ per mile.
   (i) Write down an equation for the rival's charge, $\pounds R$, in terms of $d$.
   (ii) Find the journey length for which both firms charge the same, and the cost of that journey.
   (iii) Find which firm is cheaper for a $6$-mile journey, and state one limitation of using a straight-line model.

   [6 marks]

   Total for question 4: 12 marks

End of questions