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dybincka [34]
3 years ago
8

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

Mathematics
1 answer:
juin [17]3 years ago
6 0

Answer:

y = -\frac{5}{3}x+\frac{2}{3}

Step-by-step 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 = \frac{y_2 -y_1}{x_2 -x_1}

m = \frac{-1-4}{1--2}

m = \frac{-5}{3}

The equation is then calculated using:

y = m(x - x_1) + y_1

This gives:

y =\frac{-5}{3}(x--2)+4

y =\frac{-5}{3}(x+2)+4

Open bracket

y = -\frac{5}{3}x-\frac{10}{3}+4

Take LCM

y = -\frac{5}{3}x+\frac{-10+12}{3}

y = -\frac{5}{3}x+\frac{2}{3}

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