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If f(x) is a linear function, f(−2)=4, and f(1)=−1, find an equation for f(x)

1 Answer

5 votes

Answer:


y = -(5)/(3)x+(2)/(3)

Explanation:

Given


f(-2) = 4


f(1) = -1

Required

The equation of the function

The given parameters means that:


(x_1,y_1) = (-2,4)


(x_2,y_2) = (1,-1)

Calculate the slope (m)


m = (y_2 -y_1)/(x_2 -x_1)


m = (-1-4)/(1--2)


m = (-5)/(3)

The equation is then calculated using:


y = m(x - x_1) + y_1

This gives:


y =(-5)/(3)(x--2)+4


y =(-5)/(3)(x+2)+4

Open bracket


y = -(5)/(3)x-(10)/(3)+4

Take LCM


y = -(5)/(3)x+(-10+12)/(3)


y = -(5)/(3)x+(2)/(3)

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