Question

1. Which equation shows the proportional

relationship in the table?
Time (weeks) 2 5 10
Trees Planted 130 325 650
A y = 2x
B y = 65x
C y = 130x
D y = 2x + 130
please help.

Answer 1

B.
`y = 65x`

Explanation:

Equation showing a proportional relationship between two quantities, is usually written as
`y = kx`. Where,

y = output/dependent variable

x = input/independent variable

k = constant of proportionality that exists between each pair of values given.

In this case:

y = trees planted

x = time (weeks)

To find the constant of proportionality, k, use any given pair as (x, y). Let's use (10, 650).

Substitute y = 650 and x = 10 into
`y = kx`, and solve for the value of k.

`650 = k(10)`

Divide both sides by 10

`(650)/(10) = k`

`65 = k`

`k = 65`

Substitute k = 65 into
`y = kx` to generate the equation that shows the proportional relationship in the table:

`y = 65x`