Question

The equation Y=1 1/2X represents the number of cups of dried fruit, Y. needed to make X pounds of granola. Determine whether each point would be on the graph of this proportional relationship

(1 1/2,1) (4,6) (18,12) (0,0) (2 1/2. 3 3/4 )

Answer 1

`2.\ \ (4,6)`

`4.\ \ (0,0)`

`5.\ \ (2(1)/(2),3(3)/(4))`

Explanation:

Given

`y = 1(1)/(2)x`

Required

Determine if the given points is on the graph

First,, we rewrite
`y = 1(1)/(2)x` as

`y = (3)/(2)x`

`1.\ \ (1(1)/(2),1)`

This can be interpreted as:

`x = 1(1)/(2)`

`y = 1`

Substitute
`x = 1(1)/(2)`

`y = (3)/(2) * 1(1)/(2)`

`y = (3)/(2) * (3)/(2)`

`y = (9)/(4)`

This isn't equal to the given value of y.

Hence:
`(1(1)/(2),1)` is not a point on the graph

`2.\ \ (4,6)`

Here,

`x = 4`

`y = 6`

Substitute
`x = 4`

`y = (3)/(2) * 4`

`y = (3 * 4)/(2)`

`y = (12)/(2)`

`y = 6`

This point is on the graph

`3.\ \ (18,12)`

Here,

`x = 18`

`y = 12`

Substitute
`x = 18`

`y = (3)/(2) * 18`

`y = (3 * 18)/(2)`

`y = (54)/(2)`

`y = 27`

This isn't equal to the given value of y.

Hence:
`(18,12)` is not a point on the graph

`4.\ \ (0,0)`

Here, we have

`x = 0`

`y = 0`

Substitute
`x = 0`

`y = (3)/(2) * 0`

`y = 0`

Hence:

This point is on the graph

`5.\ \ (2(1)/(2),3(3)/(4))`

Here

`x =2(1)/(2)`

`y = 3(3)/(4)`

Substitute
`x =2(1)/(2)`

`y = (3)/(2) * 2(1)/(2)`

`y = (3)/(2) * (5)/(2)`

`y = (15)/(4)`

`y = 3(3)/(4)`

Hence:

This point is on the graph