You can
put this solution on YOUR website! write an equation for the linear function
f satisfying the given conditions
1. f(3)=4 and f(0)=9
Use the slope formula:
f(x2) - f(x1)
m = ———————————————
x2 - x1
where x1 = 3 and x2 = 0
(9) - (4) 5 5
m = ——————————— = ———— = - ———
(0) - (3) -3 3
Now substitute in the point slope formula:
f(x) - f(x1) = m(x - x1)
5
f(x) - f(3) = - ———(x - 3)
3
5
f(x) - 4 = - ———(x - 3)
3
Distribute to remove the parentheses:
5
f(x) - 4 = - ———x + 5
3
Add 4 to both sides:
5
f(x) = - ———x + 9
3
2. f(2)=7 and f(8)=1
Use the slope formula:
f(x2) - f(x1)
m = ———————————————
x2 - x1
where x1 = 2 and x2 = 8
(1) - (7) -6
m = ——————————— = ———— = -1
(8) - (2) 6
Now substitute in the point slope formula:
f(x) - f(x1) = m(x - x1)
f(x) - f(2) = -1(x - 2)
f(x) - 7 = -1(x - 2)
Distribute to remove the parentheses:
f(x) - 7 = -x + 2
Add 7 to both sides:
f(x) = -x + 9
Edwin
