Question

Linear function f with the values f(-1)=8 and f(5)=6

Answer 1

Answer:

The linear function is:

$f(x) = -\frac{1}{3}x-\frac{23}{3}$

Step-by-step explanation:

Given

f(-1)=8 and f(5)=6

We can extract two pairs of input-output from the values given

From f(-1)=8,

(x1,y1) = (-1,8)

and

From f(5)=6

(x2,y2) = (5,6)

The linear function is given by:

$y = mx+b$

Here m is the slope which is calculated by the formula

$m =\frac{y_2-y_1}{x_2-x_1}$

Putting values

$m = \frac{6-8}{5+1}\\m = \frac{-2}{6}\\m = -\frac{1}{3}$

Putting in the equation

$y = -\frac{1}{3}x+b$

Putting the pair of input-output equation (5,6)

$6 = -\frac{1}{3}(5) +b\\6 = -\frac{5}{3}+b\\b = 6+\frac{5}{3}\\b = \frac{18+5}{3}\\b = \frac{23}{3}$

Putting the value of b

$y = -\frac{1}{3}x-\frac{23}{3}\\f(x) = -\frac{1}{3}x-\frac{23}{3}$

Hence,

The linear function is:

$f(x) = -\frac{1}{3}x-\frac{23}{3}$