Q7. - Algebra 2

Question

Complete parts a-c for each set of data in Exercises 6-9

1. Draw a scatter plot
2. Use two ordered pair to write a prediction equation.
3. Use your prediction equation to predict the missing value. 

6. Hockey    Each time a hockey player scores a goal, up to two teammates may be credited with assists. The table shows the number of goals and assists for some of the members of the Detroit Red Wings in the 2000-2001 NHL season.

Goals	31	15	32	27	16	20	8	4	12	12	?
Assists	45	56	37	30	24	18	17	5	10	7	15

Step-by-Step Solution

Answer

a.

b. A predicted equation is $y=1.14x+0.44$

c. The model predict that a player with 15 assists will score 13 goals.

a. Step-1 – Concept of scatter plot

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

Prediction equation – An equation of line of fit is often called a prediction equation.

Step-2 – Determine the axis.

Take goals at the x axis and assists at the y-axis, we get

$(31,45),(15,56),(32,37),(27,30),(16,24),(20,18),(8,17),(4,5),(12,10) and (12,7)$

Step-3–Constructing scatter plot.

b. Step-1 – Concept of 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 $(4,5) and (32,37)$

  $\begin{array}{l}Slope=\frac{37-5}{32-4}[\because \text{ Slope =}\frac{y_2-y_1}{x_2-x_1}]\\ =\frac{32}{28}\\ =1.14\end{array}$

Step-3 – Determine the equation.

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

Substituting values

 $\begin{array}{l}(y-5)=1.14(x-4)\\ y-5=1.14x-4.56\\ y=1.14x+0.44\end{array}$

Hence, a predicted equation is  $y=1.14x+0.44$

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 goals value for assists 15 is missing, so we substitute\[y=15\] in the predicted equation to get the value of x.

Step-3 – Calculation

$\begin{array}{l}y=1.14x+0.44\\ 15=1.14x+0.44\\ 14.56=1.14x\\ 13=x\end{array}$

Hence, the missing value is $x=13$