Question

Let f be a linear function where f(2)= -5 and f(-3)=1. Find f(x).
HOW TO DO?!?!?!?!?!

Answer 1

the general of a linear function is
f(x) = ax + b (with a and b are the constant)
now given f(2) = -5, it means
a(-2) + b = -5 or
-2a + b = -5 ........ (1)
then known the value of f(-3) = 1, it means
a(-3) + b = 1 or
-3a + b = 1 ........ (2)
now you have to solve for a and b respectively. (in the 1st and the 2nd eq)
you can solve them by elimination and subtitution method

Answer 2

got it ?

Answer 3

I still do not understand sir.

Answer 4

They gave u two points that are on the line, so you can calculate the slope

Answer 5

do u know how?

Answer 6

what are the points..?

Answer 7

They told u that f(2)= -5, which means when you plug in 2 as x, you get -5 as y, so the point (2,-5) is on the line

Answer 8

okay and the other point is (-3,1), right?

Answer 9

yep

Answer 10

u know the formula for slope?

Answer 11

You mean the point slope formula?

Answer 12

You're gonna need the slope to use that formula

Answer 13

have u ever heard of rise over run?

Answer 14

ohh i know is it (y-y1)/( x-x1)?

Answer 15

Ya thats right, so find the slope and then you can use the slope and point on the line to find the point slope form

Answer 16

the slope formula doesnt works here. like i said above we have 2 equations :
-2a + b = -5
-3a + b = 1

now, can you solve for a and b, first ?

Answer 17

Wait, i thought i was suppose to find the slope and then point slope formula to find the point slope form. What does a and b have to do with this?

Answer 18

they are the constant, and again like i said above :
the general of a linear function is f(x) = ax + b
so, we need the values of a and b, after you geot them then just plug into equation above