Linear Graphs (Cambridge International IGCSE Mathematics): Exam Questions

Line L is drawn on the grid below.

Find the equation for the straight line L.

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

On the grid, draw the graph of $y=8-2x$ for values of x from $-1$ to $4$

The equation of a straight line is $2y=3x+4.$

i) Find the gradient of this line.

ii) Find the co-ordinates of the point where the line crosses the y-axis.

( ..................... , ..................... ) [1]

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

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

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

Extract:

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

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 $y=mx+c$.

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

On the grid, draw the lines $y=x$ and $x+y=8$.

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 $AC.$

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

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 $l_{1}$.

Extract:

The line l1 has equation 2x - 3y + 12 = 0

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 $l_{2}$.

Extract:

The line l1 crosses the x-axis at the point A and the y-axis at the point B, as shown in Figure 1. The line l2 is perpendicular to l1 and passes through B.

The line $l_{2}$ crosses the $x$-axis at the point C.

Find the area of triangle ABC.