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))# ?

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Answer 1 · 2018-02-06T19:51:10

#f(t) = 62t+222#

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 #f(x)#, say #(6.2, 606.4)# and #(6.4, 618.8)# to calculate the slope #m# of the line:

#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)# in point slope form by:

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

Adding #606.4# to both ends we get:

#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 #62# being the slope and #222# the #y# intercept.