# How do you find the formula of the linear function described by the table ((t, 6.2, 6.4, 6.6, 6.8), (f(t), 606.4, 618.8, 631.2, 643.6)) ?

Feb 6, 2018

$f \left(t\right) = 62 t + 222$

#### Explanation:

Given some points of a linear function:

$\left(\begin{matrix}t & 6.2 & 6.4 & 6.6 & 6.8 \\ f \left(t\right) & 606.4 & 618.8 & 631.2 & 643.6\end{matrix}\right)$

We can take any two distinct points on the graph of $f \left(x\right)$, say $\left(6.2 , 606.4\right)$ and $\left(6.4 , 618.8\right)$ to calculate the slope $m$ of the line:

$m = \frac{\Delta y}{\Delta x} = \frac{618.8 - 606.4}{6.4 - 6.2} = \frac{12.4}{0.2} = 62$

Then we can describe the graph of $f \left(t\right)$ in point slope form by:

$f \left(t\right) - 606.4 = m \left(t - 6.2\right) = 62 \left(t - 6.2\right)$

Adding $606.4$ to both ends we get:

$f \left(t\right) = 62 \left(t - 6.2\right) + 606.4$

$\textcolor{w h i t e}{f \left(t\right)} = 62 t - 384.4 + 606.4$

$\textcolor{w h i t e}{f \left(t\right)} = 62 t + 222$

The equation:

$f \left(t\right) = 62 t + 222$

is in slope intercept form, with $62$ being the slope and $222$ the $y$ intercept.