f is a linear function such that f(1) = 0 and f(2) = 4. How do you write an equation for f(x)

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- October 21st 2009, 11:36 AMSHiFTEquation of function
f is a linear function such that f(1) = 0 and f(2) = 4. How do you write an equation for f(x)

- October 21st 2009, 11:39 AMartvandalay11
- October 21st 2009, 11:43 AMSHiFT
I'm still confused though, so do I need to come up with two of my own points then solve, or do I just solve with the variables given?

- October 21st 2009, 11:50 AMartvandalay11

You need to solve the following system of equations

1. 0=m(1)+b and

2. 4=m(2)+b

Now let's try to get you to understand this. I hand you two points, (p,q) and (r,s) and say what's the equation of the line that goes through them

You realize that all lines on the x-y plane can be written as

So you also know that for the ordered pair (p,q), the x coordinate is p and the y coordinate is q.... same for (r,s)

So since must be satisfied, you plug your points into in to get

q=mp+b and

s=mr+b

Now in a normal problem p,q,r,s will be numbers so the only "unknowns" here are m and b

You have two equations and 2 unknowns so you can solve for both m and b, and then the line you were looking for is y=mx+b

Here they tell you f(1)=0 and f(2)=4, so since f(x)=y, the points they give you are (1,0) and (2,4) - October 21st 2009, 12:08 PMmasters
- October 21st 2009, 12:18 PMartvandalay11
- October 21st 2009, 12:23 PMmasters
- October 21st 2009, 12:49 PMSHiFT
Thanks a ton guys, it makes a lot of sense now