# Find the relation between x and y, if y takes values {29,35,41,47,.......}, when x takes values {4,5,6,7,.....)?

Apr 6, 2017

Function is a linear one and $y = 6 x + 5$

#### Explanation:

Observing given numbers, $x$ takes values $\left\{4 , 5 , 6 , 7 , \ldots . .\right)$, starting from $4$ it continues to increase by $1$.

However, $y$ takes values $\left\{29 , 35 , 41 , 47.\right\}$ and starting from $29$ it continues to increase each time by $6$.

As while $x$ increases by $1$, $y$ increases by $6$,

the relation is of the type $y = 6 x + k$, a linear function.

For finding $k$, as $y$ is $29$, when $x$ is $4$, we have

$29 = 6 \times 4 + k$

or $29 = 24 + k$

or $k = 29 - 24 = 5$

Hence function is a linear one and $y = 6 x + 5$