Q4. - Algebra 2

Question

Complete parts a–c for each set of data in Exercises 4 and 5.

a. Draw a scatter plot.

b. Use two ordered pairs to write a prediction equation.

c. Use your prediction equation to predict the missing value.

Whether you are climbing a mountain or flying in an airplane, the

higher you go, the colder the air gets. The table shows the temperature in the

atmosphere at various altitudes.

Step-by-Step Solution

Answer

a. 

b. A predicted equation is $y=-0.0019x+14.8$

c. At 5000 feet , the predicted temperature $=5.3{}^{\circ } \text{C}$

(a) Step-1 – Concept of scatter plot

A scatter plot is a kind of plot where we use Cartesian coordinates to display values for typically two variables for a set of data.

Step-2 – Write given information

The table shows the temperature in the atmosphere at various altitudes.

Step-3 – Constructing scatter plot

Here, we take Altitude at the x-axis and Temperature at the y-axis, we get

(b) Step-1 – Concept of the Predicted equation

A predicted equation of a line can be used to predict one of the variables given the other variable.

Step-2 – Calculate slope

Using points (2000,11.0) and (3000, 9.1)

Slope = $\frac{9.1-11.0}{3000-2000}$   $[\because \text{ Slope =}\frac{y_2-y_1}{x_2-x_1}]$

$\begin{array}{l}=\frac{-1.9}{1000}\\ =-0.0019\end{array}$

Step-3 – Using point-slope form

Point slope form : $(y-y_1)=m(x-x_1)$

Substituting values

$\begin{array}{l}(y-11)=-0.0019(x-2000)\\ y=-0.0019x+14.8\end{array}$

Hence, a predicted equation is $y=-0.0019x+14.8$

(c) Step-1 – Use of Predicted equation

A predicted equation of a line can be used to predict one of the variables given the other variable.

Step-2 – Missing value

The temperature value for Altitude = 5000 ft is missing, so we substitute x= 5000 in the predicted equation to get the value of y.

Step-3 – Calculation

Equation becomes,

 $\begin{array}{l}y=-0.0019\left(5000\right)+14.8\\ =5.3\end{array}$

Hence, at 5000 feet , the predicted temperature $=5.3{}^{\circ } \text{C}$