Question

In 1980 approximately 4,825 million metric tons of carbon dioxide emissions were recorded for the United States. That number rose to approximately 6,000 million metric tons in the year 2005. Here you have measurements of carbon dioxide emissions for two moments in time. If you treat this information as two ordered pairs (x, y), you can use those two points to create a linear equation that helps you make predictions about the future of carbon dioxide emissions!A) Organize the measurements into ordered pairs. B) Find the slope,C) Set up an equation in point-slope form,D) Show the equation in slope-intercept form,E) Predict emissions for the year 2020,

Answer 1

ANSWER and EXPLANATION

A) To organize the measurements in ordered pairs implies that we want to put them in the form:

`(x_1,y_1);(x_2,y_2)`

Therefore, the measurements in ordered pairs are:

`\begin{gathered} (1980,4825) \\ (2005,6000) \end{gathered}`

Note: 4825 and 6000 are in millions (10⁶) of metric tons

B) To find the slope, apply the formula:

`m=(y_2-y_1)/(x_2-x_1)`

Therefore, the slope is:

`\begin{gathered} m=(6000-4825)/(2005-1980) \\ m=(1175)/(25) \\ m=47\text{ million metric tons per year} \end{gathered}`

C) To find the in point-slope form, we apply the formula:

`y-y_1=m(x-x_1)_{}`

Therefore, we have:

`y-4825=47(x-1980)`

Note: the unit is in million metric tons

D) To show the equation in point-slope form, we have to put it in the form:

`y=mx+b`

To do that, simplify the point-slope form of the equation:

`\begin{gathered} y-4825=47(x-1980) \\ y=47x-93060+4825 \\ y=47x-88235 \end{gathered}`

E) To predict the emissions for the year 2020, substitute 2020 for x in the equation above:

`\begin{gathered} y=47(2020)-88235 \\ y=94940-88235 \\ y=6705\text{ million metric tons} \end{gathered}`

That is the prediction for the year 2020.