Question

write the equation for a linear function that satisfies the given conditions f(1)=2 and f(5)=7

Answer 1

f(x) changes by 7-2 = 5 when x changes by 5-1 = 4, so the slope is 5/4. Using point-slope form the equation of the line can be written as
.. y = (5/4)(x -1) +2
Rearranging, this becomes
.. y = (5/4)x +3/4

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In standard form, it is
.. 5x -4y = -3