Question

Prepare a table of values showing the co-ordinates of the points highlighted on each of the graphs given below. hence, write the equation showing the relation between x and y.

figure

Answer 1

The table for the graph of Fig. 5.34(a) is shown below :

x	1	$-$1	$-$2
y	$-$1	3	5

The given graph is of a straight line.
We know that the equation of a straight line is

ax + by = c, where (x,y) are the co-ordinates of the point.

Now, it passes through (1, $-$1), ($-$1,3) and ($-$2,5).
Therefore, putting these values in the equation, we get:
a $-$ b = c .............(1)
$-$a+3b=c .............(2)
$-$2a+5b=c ..........(3)
From (1) + (2), we get:
b = c ---------(4)
From (2) $-$ (3), we get:
a = 2b ----------(5)
Now equation of the line, using (4) and (5), is
2bx + by = b
$\Rightarrow 2x+y=1$

The table for the graph of Fig. 5.34(b) is shown below :

x	$-$1	2	3
y	$-$2	1	2

The given graph is of a straight line.
We know that the equation of straight line is

ax + by = c, where (x,y) are the co-ordinates of the point.

Now, it passes through ($-$1,$-$2), (2,1) and (3,2).
Therefore putting these values in the equation, we get:
$-$a $-$ 2b = c .............(6)
2a+b = c .............(7)
3a+2b = c ..........(8)
From 2$\times$(6) + (7), we get:
$-$b = c ---------(9)
From (7) $-$ (8), we get:
$-$a = b ----------(10)
Now, equation of the line using (9) and (10), is
$-$bx + by = $-$b
$\Rightarrow x-y=1$