Question

Sam the Hummingbird flies at a rate of 2 yards per minute, as modeled by the equation y = 2x. She

increases her rate by 2 yards per minute. Plot two ordered pairs showing the distances she will fly at 1

minutes and 2 minutes, respectively, at her new rate.

Sometimes she may move backwards.

Answer 1

See attachment for plot

Explanation:

Given

`y =2x`

`R =+2` --- increment in the rate

First, we need to model the new rate

A linear equation is:

`y = mx + b`

Where

`m = rate`

Compare
`y =2x` and
`y = mx + b`. we have:

`m =2`

The above represents the previous rate.

The new rate:

`R =+2`

Rewrite as:

`R = m+2`

`R = 2+2`

`R = 4`

So, the model is:

`y = Rx`

`y = 4x`

The plot at 1 and 2 minutes

When
`x = 1`

`y = 4x = 4 * 1 = 4`

When
`x = 2`

`y = 4x = 4 * 2 = 8`

So, we have:

`(x_1,y_1) =(1,4)`

`(x_2,y_2) =(2,8)`

Whether she moves backwards or forward, the distance covered remains the same

See attachment for plot