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 $a$ and $b$.
State a linear relationship between the variables $x$ and $y$.

• A. $a=5$, $b=9$. Linear relation is $y=\frac{x+1}{2}$
• B. $a=3$, $b=9$. Linear relation is $y=\frac{x+1}{2}$
• C. $a=0$, $b=9$. Linear relation is $y=\frac{x+1}{2}$
• D. $a=7$, $b=9$. Linear relation is $y=\frac{x+1}{2}$

Answer 1

Answer: (C)

$a=0$, $b=9$. Linear relation is $y=\frac{x+1}{2}$

Plotting the above table in the graph
Now,

From graph when $x=-1$, $y=0$
and when $y=5$, $x=9$

$\therefore a=0,b=9$

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=$\frac{1}{2}$
$c=\frac{1}{2}$
$m=\frac{y_2-y_1}{x_2-x_1}$ ...[ two points on the line]
$=>m=\frac{2-(-2)}{3-(-5)}$

$=>m=\frac{4}{8}$
$=>m=\frac{1}{2}$
$y=mx+c$
$=>y=\frac{1}{2}x+\frac{1}{2}$
$=>y=\frac{x+1}{2}$