The function that represents her savings is the linear function f(x) = 40x; after 7 years she would have saved $280.
Explanation
We can see that this data is increasing by the same amount every time; this means it is linear.
Since it is linear, it has a slope. We find this using the formula
m=(y₂-y₁)/(x₂-x₁)
m=(80-40)/(2-1) = 40/1 = 40
We can now use this and the first point to write our equation in point-slope form:
y-y₁=m(x-x₁)
y-40=40(x-1)
Using the distributive property,
y-40=40*x-40*1
y-40=40x-40
Add 40 to both sides:
y-40+40=40x-40+40
y=40x
For 7 years, we replace x with 7: 40*7=280
