Question

Use the table given below to draw the graph.

$x$	$-5$	$-1$	$3$	$b$	$13$
$y$	$-2$	$a$	$2$	$5$	$7$

From your graph, find the values of ${}^{\prime }{a}^{\prime }$ and ${}^{\prime }{b}^{\prime }$.
State a linear relation between the variables $x$ and $y$.

Answer 1

When $x=-1,y=0$. i.e., $a=0$.
When $y=5,x=9$. i.e., $b=9$.
Let $y=px+q....\left(1\right)$
be a linear relation between $x$ and $y$
Substitute $x=9$ and $y=5$ in the equation (1), we have,
$5=9p+q....\left(2\right)$
Substitute $x=-1$ and $y=0$ in the equation (1), we have,
$0=-p+q....\left(3\right)$
Subtracting (3) from (2), we have,
$5=10p$
$\Rightarrow p=\frac{5}{10}$
$\Rightarrow p=\frac{1}{2}$
From (3), we have;
$p=q$
$\therefore q=\frac{1}{2}$
Thus, the linear relation is
$y=px+q$
$\Rightarrow y=\frac{1}{2}x+\frac{1}{2}$
$\Rightarrow y=\frac{x+1}{2}$.