Equation of a straight lineEdexcel International A Level Maths: Subtopic test

1. 1
   A line $l$ passes through the points $A(2,5)$ and $B(6,13)$.

   (a)

   Find the gradient of $l$.

   [1 mark]

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

   (b)

   Which of the following is an equation of $l$?

   [1 mark]

   • A$y=2x+5$
   • B$y=2x-1$
   • C$y=2x+9$
   • D$y=2x+1$

   (c)

   Find the coordinates of the point where $l$ meets the $x$-axis.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The line $m$ has equation $3x-4y+8=0$.

   (a)

   Find the gradient of $m$.

   [1 mark]

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

   (b)

   Find the $y$-intercept of $m$.

   [1 mark]

   • A$8$
   • B$-2$
   • C$2$
   • D$-\frac83$

   (c)

   Find the $x$-coordinate of the point on $m$ where $y=7$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A line $l_1$ passes through the points $P(-3,4)$ and $Q(5,-2)$.

   (a)

   Find an equation of the line $l_1$, giving your answer in the form $ax+by+c=0$, where $a$, $b$ and $c$ are integers.

   [3 marks]

   (b)

   The line $l_1$ meets the $x$-axis at $A$ and the $y$-axis at $B$. Find the area of triangle $OAB$, where $O$ is the origin.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Triangle $ABC$ has vertices $A(1,2)$, $B(7,4)$ and $C(5,10)$.

   (a)

   (i) Find an equation of the line $AB$, in the form $ax+by+c=0$ where $a$, $b$ and $c$ are integers.
   (ii) The midpoint of $AB$ is $M$. Find an equation of the line $CM$, in the form $y=mx+c$.

   [6 marks]

   (b)

   The line $AB$ meets the $x$-axis at $D$ and the line $BC$ meets the $x$-axis at $F$. Find the area of triangle $CDF$.

   [6 marks]

   Total for question 4: 12 marks

End of questions