Question

Write a linear function f with the values f(10)=5 and f(2)=-3

Answer 1

Answer:

$f(x)=x-5$

Step-by-step explanation:

step 1

Find the slope m

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have the ordered pairs

(10,5) and (2,-3)

substitute the values

$m=\frac{-3-5}{2-10}$

$m=\frac{-8}{-8}$

$m=1$

step 2

Find the equation of the line in slope intercept form

$f(x)=mx+b$

we have

$m=1$

$point\ (10,5)$

substitute and solve for b

$5=(1)(10)+b$

$5=10+b$

$b=-5$

The linear function is equal to

$f(x)=x-5$