For exercises 30-32, use the table that shows the amount Americans spent on recreation in recent years.

31. Write a prediction equation

The slope of a line is the ratio of the change in the y-coordinates to the change in the x- coordinates.

Symbolically, the slope m of the line passing through the points $\left(x_1,y_1\right)\text{and}\left(x_2,y_2\right)$ is given by $m=\frac{y_2-y_1}{x_2-x_1}$ where $x_1\ne x_2$.

The slope-intercept form of the equation of a line is given by $y=mx+b$ where mis the slope and bis the y-intercept.

The point slope form of a equation of a line is given by $y-y_1=m(x-x_1)$where $\left(x_1,y_1\right)$are the coordinates of a point on the line and m is the slope of the line.

A prediction equation is an equation which is used to predict one of the variables given the other variable.

In order to find a prediction equation for a set of data, select two points that appear to represent the data well.

Let x represents the number of years since 1995. Therefore take the number of years since 1995 on the horizontal axis and amount on the vertical axis.

From the table find the ordered pairs which are as follows:

$\left(1995,401.6\right),\left(1996,429.6\right),\left(1997,457.8\right),\left(1998,494.7\right)$

The scatter plot is as shown below:

A scatter plot suggests that any two points can be used to find a prediction equation. Hence use $\left(1995,401.6\right)\text{and}\left(1996,429.6\right)$.

Therefore, the slope is obtained as follows:

By using the value of slope in point slope form the equation is obtained in slope intercept form as follows:

Keep the variable y on one side and the rest on other side. Hence,

Hence the equation is obtained in slope intercept form and this is one prediction equation.