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Write a linear function with f(3=7 and f(1)=17

User Tom Droste
by
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1 Answer

5 votes

Answer:

y = - 5x + 22

Explanation:

A linear equation has the form

y = mx + c ( m is the slope and c the y- intercept )

to obtain the equation we require to find m and c

given

f(3) = 7 , means when x = 3 then y = 7

f(1) = 17 , means when x = 1 then y = 17

substitute these values into the equation to obtain a pair of simultaneous equations

7 = 3m + c → (1)

17 = m + c → (2)

subtract (2) from (1) term by term to eliminate c

7 - 17 = (3m - m) + (c - c)

- 10 = 2m + 0

- 10 = 2m ( divide both sides by 2 )

- 5 = m

substitute m = - 5 into (1) and solve for c

7 = 3(- 5) + c

7 = - 15 + c ( add 15 to both sides )

22 = c

now substitute the values for m and c into the linear equation

y = - 5x + 22

User Andreas Herd
by
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