How do you write a linear function f with the values #f(2)=-1# and #f(5)=4#?

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Answer 1 · 2017-01-01T23:54:21

Use the two points to compute the slope, m, then use one of the points in the form #y = m(x) + b# to find the value of b.

The equation for the slope, m, of a line is:

#m = (y_1 - y_0)/(x_1 - x_0)" [1]"#

The equation #f(2) = -1# tells us that #x_0 = 2 and y_0 = -1#; substitute this into equation [1]:

#m = (y_1 - -1)/(x_1 - 2)" [2]"#

The equation #f(5) = 4# tells us that #x_1 = 5 and y_1 = 4#; substitute this into equation [2]:

#m = (4 - -1)/(5 - 2)" [3]"#

#m = 5/3#

Substitute #5/3# for m into the equation #y = m(x) + b#

#y = 5/3x + b" [4]"#

Substitute 2 for x and -1 for y and the solve for b:

#-1 = 5/3(2) + b#

#b = -13/3#

Substitute #-13/3# for b in equation [4]:

#y = 5/3x -13/3" [5]"#

Check:

#-1 = 5/3(2) -13/3#
#4 = 5/3(5) - 13/3#

#-1 = -1#
#4 = 4#

This checks

Equation [5] is the answer.