Question

Margaret and Donovan are twins. They

have each kept track of their heights
every year since they were 5.
Margaret made a table to track her
height.
Age, a 5 | 6 | 7
Height, h (cm) 101 105 109
|
8
113
| 9
| 117
| 10
| 121
Donovan wrote an equation to track his height: h = 5a + 84
Which statement correctly compares the twins' rates of growth?

Answer 1

The rate of a linear function is its slope.

The slope is defined via the "rise over run" ratio, i.e.

`m = (\Delta y)/(\Delta x) = (y_2-y_1)/(x_2-x_1)`

If you pick any two columns from the table and perform this operation (for example the first two), you have

`m = (y_2-y_1)/(x_2-x_1) = (105-101)/(6-5)=4`

On the other hand, given an equation like
`y=mx+b`, the slope is the coefficient m. So, the rate of
`y=5a+84` is 5.

This means that Margaret grows 4cm per year, while Donovan grows 5cm per year, and therefore he grows faster.