# Find the relation between points (-4,19), (0,5) and (3,-5.5)?

Jan 24, 2018

$y = - 3.5 x + 5$

#### Explanation:

Let us first consider the points $\left(- 4 , 19\right)$ and $\left(0 , 5\right)$

$-$ as $x$ increases by $4$, $y$ decreases by $14$ i.e. $\frac{14}{4} = 3.5$ for each unit of $x$

between points $\left(0 , 5\right)$ and $\left(3 , - 5.5\right)$

$-$ as $x$ increases by $3$, $y$ decreases by $10.5$ i.e. $\frac{10.5}{3} = 3.5$ for each unit of $x$

again between points $\left(3 , - 5.5\right)$ and $\left(5 , - 12.5\right)$

$-$ as $x$ increases by $2$, $y$ decreases by $7$ i.e. $\frac{7}{2} = 3.5$ for each unit of $x$

We observe that

• when $x$ increases, $y$ decreases.

• for $x = 0$, we have $y = 5$ and

• for each unit increase in value of $x$, increase in value of $y$ is $3.5$

Hence relation is $y = - 3.5 x + 5$