Question

There are 52 blades of grass in 2 in^2 of lawn. there are 580 blades of grass in 8 in^2 of the same lawn. which equation models the y blades of grass found in x in^2 of lawn?

A) y=-88x-124
B) y=-88x+124
C) y=88x-124
D) y=88x+24

Answer 1

The correct option is C.

Explanation:

It is given that there are 52 blades of grass in 2 in^2 of lawn and there are 580 blades of grass in 8 in^2 of the same lawn.

It means the line passing though the points (2,52) and (8,580).

If a linear function passing through two points then the equation of line is

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

The function passing though the points (2,52) and (8,580), so the required equation is

`y-52=(580-52)/(8-2)(x-2)`

`y-52=88(x-2)`

`y-52=88x-176`

`y=88x-176+52`

`y=88x-124`

The equation
`y=88x-124` models the y blades of grass found in x in^2 of lawn.

Therefore the correct option is C.

Answer 2

y - 52 = (580 - 52)/(8 - 2) (x - 2)
y - 52 = 528/6 (x - 2) = 88(x - 2)
y = 88x - 176 + 52
y = 88x - 124