Use the table given below to draw the graph. x -5 -1 3 b 13 y -2 … - Vidyadip

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 $y$.

✓

Answer

The table is:

$X$	$- 5$	$- 1$	$3$	$b$	$13$
$Y$	$- 2$	$a$	$2$	$5$	$7$

Plotting the points as shown in the above table, we get the following required graph:

When $x = - 1$, then $y = 0$
$\Rightarrow a = 0$
When $y = 5$, then $x = 9$
$\Rightarrow b = 9$

Let $y = px + q\dots....(1)$
be a linear relation between$x$ and $y$
Substitute $x = 9$ and $y = 5$ in the equation $(1)$, we have,
$5 = 9p + q\dots....(2)$
Substitute $x = - 1$ and $y = 0$ in the equation $(1)$, we have,
$0 = - p + q \dots....(3)$
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
$y = px + q$
$\Rightarrow y =\frac{1}{2} x+\frac{1}{2}$
$\Rightarrow y =\frac{x+1}{2}$

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