Question

Every week Ben collects a few pounds of paper to recycle. The graph below shows the total number of pounds of paper(y) that Ben collected in a certain amount of time (x), in weeks:

Answer 1

To obtain the amount of paper that would most likely be collected in 10 weeks, the following steps are necessary:

Step 1: Select two points that lie on the straight line and use the two points to derive the equation of the straight line, as follows:

Such two points could be: (x1, y1) = (0, 30) and (x2, y2) = (120, 3)

Using the following formula, we can derive the equation of the straight line:

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

Thus:

`\begin{gathered} (y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1) \\ \Rightarrow\frac{y-30_{}}{x-0_{}}=\frac{120_{}-30_{}}{3_{}-0_{}} \\ \Rightarrow\frac{y-30_{}}{x_{}}=\frac{90_{}}{3_{}_{}} \\ \Rightarrow\frac{y-30_{}}{x_{}}=30 \\ \Rightarrow y-30=30* x \\ \Rightarrow y=30x+30 \end{gathered}`

The above equation can be re-written as:

`\begin{gathered} y=30x+30 \\ \Rightarrow\text{Amount of paper collected = 30 }* number\text{ of w}eeks\text{ + 30 } \end{gathered}`

Step 2: Use the derived equation to obtain the value of the amount of paper collected in 10 weeks, as follows:

In 10 weeks, we will have :

`\begin{gathered} \text{Amount of paper collected = 30 }* number\text{ of w}eeks\text{ + 30 } \\ \Rightarrow\text{Amount of paper collected = 30 }*10\text{ + 30 } \\ \Rightarrow\text{Amount of paper collected = 300 + 30 }=330 \\ \Rightarrow\text{Amount of paper collected = 3}30 \end{gathered}`

Therefore, the amount of paper that would most likely be collected in 10 weeks is 330