Question

Write an equation for the relationship shown in the table. #7

Answer 1

Statement Problem: Write an equation for the relationship shown in the table below.

Solution:

First, we observed that as the variable x is increasing, then the variable y is also increasing. Thus, x is directly proportional to y. Then, it shows a linear proportion. We have;

`\begin{gathered} y=mx+b\ldots\ldots\ldots....\mathrm{}\text{equation (i)} \\ x=14,y=5 \\ 5=14m+b\ldots\ldots\ldots\ldots\text{.equation 1} \\ Also,x=20,y=11 \\ 11=20m+b\ldots\ldots\ldots\text{.equation}2 \end{gathered}`

Thus, we would solve equation 1 and equation 2 simultaneously.

Subtract equation 1 from equation 2.

`\begin{gathered} \text{equation}2\text{ - equation1} \\ 11-5=20m-14m+b-b \\ 6=6m \\ \text{Divide both sides of the equation by 6;} \\ (6)/(6)=(6m)/(6) \\ m=1 \end{gathered}`

Then, substitute the value of m in equation 1.