Question

The given table represents a linear function.

$x$	$y$
$-1$	$-3$
$0$	$2$
$3$	$p$
$q$	$27$

Find the value of $(p+q)$?

• A. $17$
• B. $18$
• C. $22$
• D. $27$

Answer 1

The correct option is C $22$

We know that, in a linear function, the slope is constant for any two points on the line.

The slope between the first and the second points $=\frac{(2-(-3\left)\right)}{(0-(-1\left)\right)}=\frac{(2+3)}{(0+1)}=\frac{5}{1}=5$

The slope between the second and the third points $=\frac{(p-2)}{(3-0)}=\frac{(p-2)}{3}$

The slope between the third and the fourth points $=\frac{(27-p)}{(q-3)}$

Given: The function is linear.
Hence, the slope will be constant for any two points on the line.

So,
$5=\frac{(p-2)}{3}$
$\Rightarrow 5\times 3=(p-2)$
$\Rightarrow 15=(p-2)$
$\Rightarrow p=15+2$
$\Rightarrow p=17$

We know the slope between the third and the fourth points
$=\frac{(27-p)}{(q-3)}=\frac{(27-17)}{(q-3)}=\frac{10}{(q-3)}$

Now,
$\frac{10}{(q-3)}=5$
$\Rightarrow 10=5\times (p-3)$
$\Rightarrow 10=5p-15$
$\Rightarrow 10+15=5q$
$\Rightarrow q=\frac{25}{5}=5$

Hence,
$p+q=17+5=22$.

Option C is correct.