Question

Ming wrote the table of points below. x y 5 10 10 20 15 30 Which explains whether or not Ming has described a proportional relationship, and why? Ming has described a proportional relationship because the ordered pairs are linear and the line passes through the origin. Ming has not described a proportional relationship. Although it is a linear relationship, it does not pass through the origin. Ming has not described a proportional relationship. Although it passes through the origin, it is not a linear relationship. Ming has described a proportional relationship because the line does not pass through the origin.

Answer 1

This is a proportional relationship.

If you drew the points and made a line, it would pass through the origin. Also, all you need to do is multiply the x value by 2 and you have the y-value.

Answer 2

Option A.

Explanation:

The given table is

x y

5 10

10 20

15 30

From the given table it is clear that the value of y increases by 10 when the value of x increases by 5. It means the rate of change is constant.

So, the given table represents a linear relationship.

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

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

The linear function passes through (5,10) and (10,20), so the equation of line is

`y-10=(20-10)/(10-5)(x-5)`

`y-10=2(x-5)`

`y-10=2x-10`

`y=2x`

For x=0,

`y=2(0)=0`

It means it passes through the origin, i.e., (0,0).

Ming has described a proportional relationship because the ordered pairs are linear and the line passes through the origin.

Therefore, the correct option is A.