Question

Which explains whether or not Ming has described a proportional relationship, and why?

Answer 1

Answer:

Ming has described a proportional relationship because the ordered pairs are linear and the line passes through the origin. Although it is a linear relationship, it does not pass through the origin. Ming has not described a proportional relationship.

Step-by-step explanation:

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Answer 2

Answer:

The correct option is (A). Ming has described a proportional relationship because the ordered pairs are linear and also the line passes through the origin.

Step-by-step explanation:

The given table is

$\begin{array}{ll}x& y\\ 5& 10\\ 10& 20\\ 15&30\end{array}$

From the given table it's clear that the worth of$y$ increases by $10$ when the worth of $x$ increases by $5.$ It means the speed of change is constant.

So, the given table represents a linear relationship.

If a linear function passes through the 2 points then the equation of line is

$y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{1})$

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

$\begin{aligned}y-10&=\frac{20-10}{10-5}(x-5)\\ y-10&=\frac{10}{5}(x-5)\\ y-10&=2x-10\\ y&=2x\end$

For $x=0$,

$y=2(0)\\y=0$

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

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

Hence, the right option could be A.

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