Q. 18 - Precalculus Enhanced with Graphing Utilities

Question

Raisins The following data represent the weight (in grams) of a box of raisins and the number of raisins in the box.

(a) Draw a scatter diagram of the data treating weight as the independent variable.

(b) What type of relation appears to exist between the weight of a box of raisins and the number of raisins?

(c) Select two points and find a linear model that contains the points.

(d) Graph the line on the scatter diagram drawn in part (b).

(e) Use the linear model to predict the number of raisins in a box that weighs 42.5 grams.

(f) Interpret the slope of the line found in part (c).

Step-by-Step Solution

Answer

(a). The scatter diagram of the data treating weight as the independent variable is 

(b). The relation does not exist.

(c). Equation of the line is  y=86.

(d). The graph of the line on a scatter plot is,

(e). The linear model to predict the number of raisins

in a box that weighs 42.5 grams is 86.

(f). The slope of the line in part (c) is zero.

Part (a) Step 1. Given information

The given data is 

Part (a) Step 1. Draw the scatter plot.

The scatter plot of the given data is,

Part (b) Step 1. Relation appears to exist between the weight of a box of raisins and the number of raisins.

The relation between weight and the number of raisins does not exist because the second column (Number of raisins) has two different values for the one same values in the column first (Weight). The value 42.3 has 87 and and 82, two different values. Thus, the relation does not exist.

Part (c) Step 1. Equation of line.

Take two points from the given table:

$\left(42.3,87\right) \mathrm{and} \left(42.4,87\right)$

Now, equation of line passing through two points is,

$$\begin{gathered} \left(y-87\right)=\frac{87-87}{42.4-42.3}\left(x-42.4\right) \\ \Rightarrow y-87=0 \\ \Rightarrow y=87 \end{gathered}$$

Thus, the equation of the line is y= 87. The equation may be changed as the point will change.  

Part (d) Step 1. Draw the model graph.

Consider the obtained model and draw it.

Part (e) Step 1. Find the value of the model.

Using the linear model to predict the number of raisins in a box that weighs 42.5 grams.

Now, the number of raisins in a box that weighs 42.5 grams is 86.

Part (f) Step 1. Explain the Slope.

The equation of the line is y=87. Thus, the value of the slope of the line is zero. This statement depends on the linear model. As the model will change, the slope will work accordingly.