Question

The equation y = \large 1\frac{1}{2}x 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. Choose true or false for each point

Answer 1

`(1(1)/(2),1)` - False

`(4,6)` - True

`(18,12)` -- False

`(0,0)` -- True

`(2(1)/(2),3(3)/(4))` -- True

Explanation:

The points are

`(1(1)/(2),1)` ,
`(4,6)`,
`(18,12)`,
`(0,0)` and
`(2(1)/(2),3(3)/(4))` ---- missing from the question

Given

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

Required

Determine if each of the points would be on
`y = 1(1)/(2)x`

To do this, we simply substitute the value of x and of each point in
`y = 1(1)/(2)x`.

(a)
`(1(1)/(2),1)`

In this case;

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

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

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

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

`y = (9)/(4)`

`y = 2(1)/(4)`

The point
`(1(1)/(2),1)` won't be on the graph because the corresponding value of y for
`x = 1(1)/(2)` is
`y = 2(1)/(4)`

(b)
`(4,6)`

In this case;

`x = 4`

`y = 6`

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

`y = 1(1)/(2) * 4`

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

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

`y = (12)/(2)`

`y = 6`

The point
`(4,6)` would be on the graph because the corresponding value of y for
`x = 4` is
`y = 6`

(c)
`(18,12)`

In this case:

`x = 18;y = 12`

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

`y = 1(1)/(2) * 18`

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

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

`y = (54)/(2)`

`y = 27`

The point
`(18,12)` wouldn't be on the graph because the corresponding value of y for
`x = 18` is
`y = 12`

(d)
`(0,0)`

In this case;

`x =0; y = 0`

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

`y = 1(1)/(2) * 0`

`y = 0`

The point
`(0,0)` would be on the graph because the corresponding value of y for
`x = 0` is
`y = 0`

(e)
`(2(1)/(2),3(3)/(4))`

In this case:

`x = 2(1)/(2)`;
`y = 3(3)/(4)`

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

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

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

`y = (15)/(4)`

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

The point
`(2(1)/(2),3(3)/(4))` would be on the graph because the corresponding value of y for
`x = 2(1)/(2)` is
`y = 3(3)/(4)`