Linear Graphs (Cambridge (CIE) O Level Maths): Exam Questions

A straight line, $l$, has equation $y=5x+12$.

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

( ....................... , ......................)

A line perpendicular to line $l$ has gradient $k$.  
Find the value of $k$.  

$k=$................................................

On the diagram,

Sketch the graph of $y=\frac{1}{2}x+1$.

A line joins $A(1,3)$ to $B(5,8)$.

Find the equation of the line $AB$.

Give your answer in the form $y=mx+c$.

$y$ = ...................................................

A is the point (7, 2) and B is the point (−5, 8).

Find the equation of the line that is perpendicular to AB and that passes through the point (−1, 3).
Give your answer in the form $y=mx+c$.

$y$ = ..............................................

A line from the point (2, 3) is perpendicular to the line $y=\frac{1}{3}x+1$. The two lines meet at the point $P$.

Find the coordinates of $P$.

( ...................... , ...................... )

A is the point $(2,3)$ and B is the point $(7,-5)$.

Find the equation of the line through A that is perpendicular to AB.
Give your answer in the form $y=mx+c$.  

$y=$....................................................

P is the point (16, 9) and Q is the point (22, 24).

Find the equation of the line perpendicular to PQ that passes through the point (5, 1).
Give your answer in the form $y=mx+c$.

$y=$................................................

A rhombus $ABCD$ has a diagonal $AC$ where $A$ is the point $(-3,10)$ and C is the point $(4,-4).$

i) Calculate the length $AC.$

[3]

ii) Show that the equation of the line $AC$ is  $y=-2x+4.$

[2]

Find the equation of the line $BD.$

The coordinates of P are $(-3,8)$ and the coordinates of Q are $(9,-2)$.

Find the equation of the perpendicular bisector of PQ.  

The coordinates of P are $(-3,8)$ and the coordinates of Q are $(9,-2)$.

Find the equation of the line parallel to PQ that passes through the point $(6,-1)$.  

A straight line joins the points $A$ (-2, -3) and $C$ (1, 9).

Find the equation of the line $AC$ in the form $y=mx+c$.  

$y$ = ..............................................

$ABCD$ is a kite, where $AC$ is the longer diagonal of the kite. $B$ is the point (3.5, 2).

i) Find the equation of the line $BD$ in the form $y=mx+c$.  

$y$ = .............................................. [3]

ii) The diagonals $AC$ and $BD$ intersect at (-0.5, 3).   Work out the co-ordinates of $D$.  

(...................... , ....................) [2]

Figure 1

The line $l_1$ has equation $2x-3y+12=0$
Find the gradient of $l_1$.

The line $l_1$ crosses the x-axis at the point A and the y-axis at the point B, as shown in Figure 1.

The line $l_2$ is perpendicular to $l_1$ and passes through B.

Find an equation of $l_2$.

The line $l_2$ crosses the $x$-axis at the point C.

Find the area of triangle ABC.