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Question

Determine the linear function whose graph is a line that contains the points (7, 4) and (1, -3)

A
76x+256
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B
76x+256
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C
16x+256
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D
76x256
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Solution

The correct option is C 76x256
Using f(x)=ax+b to represent the linear function, we know that for this problem
f(7)=7a+b=4 and f(1)=a+b=3. Thus, we have the following system to solve
7a+b=4 ......... (1)
a+b=3 ......... (2)
Eq. (2) can be replaced with an eq. formed by multiplying eq. (1) by -1 and adding that result to eq. (2)
7a+b=4 ......... (3)
6a=7 ............ (4)
From eq (4) we can find that a = 7/6. Then we can substitute 7/6 for a in eq. (2)
a+b=3
76+b=3;b=376b=256
The linear function is f(x)=76x256

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