Question

The table below shows the amount of money, in thousands of dollars, Amelia has saved after different numbers of years:

Years (x) 1 2 3 4 5 6
Money (y) (thousands of dollars) 40 80 120 160 200 240


Identify the function that represents Amelia's savings and the amount that Amelia will have saved in 7 years.

Answer 1

Having just took the test I can confirm your answer is C!

Answer 2

The function that represents her savings is the linear function f(x) = 40x; after 7 years she would have saved $280.

Step-by-step 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