Question

Use a graphing calculator to graph the points. Which type of model best fits the data? $$-(-3,4),\left(-2, \frac{7}{2}\right),(-1,3),\left(0, \frac{5}{2}\right),(1,2),\left(2, \frac{3}{2}\right),(3,1)$$

Short answer

The best-fit model for this data set is linear.

Step-by-step solution

Enter the points into the calculator

First, you need to input each of the points (-3,4), (-2, \(\frac{7}{2}\)), (-1,3), (0, \(\frac{5}{2}\)), (1,2), (2, \(\frac{3}{2}\)), and (3,1) into your graphing calculator.

Plot the points

Once the points are entered, each point needs to be individually plotted on the graph in the calculator. This will give a visual representation of how the points are distributed.

Identify the pattern

After the points have been plotted, you should try to identify any patterns or trends. Look at the relationship between the x-values and corresponding y-values.

Determine the model type

Based on this pattern, you need to determine which type of mathematical model (linear, quadratic, exponential, etc) best fits the distributed data points. In this case, the pattern indicates a linear decrease as the x-value increases. So, a linear model is most suitable for this data set.