# 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))# ?

##### 1 Answer

Feb 6, 2018

#### Explanation:

Given some points of a linear function:

#((t, 6.2, 6.4, 6.6, 6.8), (f(t), 606.4, 618.8, 631.2, 643.6))#

We can take any two distinct points on the graph of

#m = (Delta y)/(Delta x) = (618.8 - 606.4)/(6.4 - 6.2) = 12.4/0.2 = 62#

Then we can describe the graph of

#f(t) - 606.4 = m(t - 6.2) = 62(t-6.2)#

Adding

#f(t) = 62(t-6.2)+606.4#

#color(white)(f(t)) = 62t-384.4+606.4#

#color(white)(f(t)) = 62t+222#

The equation:

#f(t) = 62t+222#

is in slope intercept form, with