Question
Asked Sep 22, 2019

A linear function is such that ?(3) = 8 and ?(−2) = 2. Find the formula for the linear function.

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Expert Answer

Step 1

Let the linear function be f(x)=ax+b

Since , we have f(3)=8 and f(-2)=2, so we have two equation in x

f(x)- ах +b
Г(3) -8
— За + b %3D 8
г(-2)-2
3-2а+b%3D 2
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Image Transcriptionclose

f(x)- ах +b Г(3) -8 — За + b %3D 8 г(-2)-2 3-2а+b%3D 2

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Step 2

On solving these equations , we get the values a and b.

3a+b--2a b) 8-2
6
5a 6 a-
5
6
b = 8- 3a = 8 -3x -
5
40 18 22
3ab 8
5
5
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Image Transcriptionclose

3a+b--2a b) 8-2 6 5a 6 a- 5 6 b = 8- 3a = 8 -3x - 5 40 18 22 3ab 8 5 5

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Step 3

On substituting the values of a and ...

f(x)=ax +b
6
-X
22
f(x)
5
5
help_outline

Image Transcriptionclose

f(x)=ax +b 6 -X 22 f(x) 5 5

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Math

Algebra

Equations and In-equations