Question

The table shows the side lengths and perimeters of four squares. Side Length (x) Perimeter (y) 4.5 18 8.5 34 10.25 41 13.75 55 Which equation represents the relationship between the side length, x, and the perimeter, y?

Answer 1

y=4x

Explanation:

Answer 2

The equation will be:
`y=4x`

Explanation:

Side lengths
`(x)` ⇒ 4.5 8.5 10.25 13.75

Perimeter
`(y)` ⇒ 18 34 41 55

First we will pick any two ordered pairs in form of point like
`(x,y)`. So, here
`(x_(1), y_(1))= (4.5, 18)` and
`(x_(2), y_(2))= (8.5, 34)`

Now, the slope will be:
`m= (y_(2)-y_(1))/(x_(2)-x_(1))= (34-18)/(8.5-4.5)=(16)/(4)=4`

So, the equation using the point-slope form will be..............

`y-y_(1)=m(x-x_(1))\\ \\ y-18=4(x-4.5)\\ \\ y-18=4x-18\\ \\ y=4x`

Thus, the equation that represents the relationship between the side length
`(x)` and the perimeter
`(y)` will be:
`y=4x`