Question

Draw the graph obtained from the table below:

$x$	$a$	$3$	$-5$	$5$	$c$	$-1$
$y$	$-1$	$2$	$b$	$3$	$4$	$0$

Use the graph to find the values of $a,b$ and $c$. State a linear relation between the variables $x$ and $y$.

• A. $a=-3$; $b=-2$, $c=7$. Linear relation is $x=2y-1$
• B. $a=-2$; $b=-2$, $c=7$. Linear relation is $x=2y-8$
• C. $a=-1$; $b=-2$, $c=7$. Linear relation is $x=2y-5$
• D. $a=9$; $b=-2$, $c=7$. Linear relation is $x=y-1$

Answer 1

The correct option is A $a=-3$; $b=-2$, $c=7$. Linear relation is $x=2y-1$

$x$	$a$	$3$	$-5$	$5$	$c$	$-1$
$y$	$-1$	$2$	$b$	$3$	$4$	$0$

Plotting the above table in the graph
Now,
From graph when $y=-1$, $x=-3$
and when $x=-5$, $y=-2$
when $y=4$, $x=7$
$\therefore a=-3,b=-2,c=7$
Let the linear equation be $y=mx+c$
Where, $m$ is the slope of the line
and $c$ is the $y$ intercept .
From the graph at $x=0,y=\frac{1}{2}$
$y$ intercept=$\frac{1}{2}$
$c=\frac{1}{2}$
$m=\frac{y_2-y_1}{x_2-x_1}$ [slope formula for two points on the line]
$\Rightarrow m=\frac{3-2}{5-3}$
$\Rightarrow m=\frac{1}{2}$
$y=mx+c$
$\Rightarrow y=\frac{1}{2}x+\frac{1}{2}$
$\Rightarrow y=\frac{x+1}{2}$