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