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From 1990 through 2003, the amounts $A$ (in millions of dollars) spent on skiing equipment in the United States are shown in the table, where $t$ represents the year. Sketch a scatter plot of the data. (Source: National Sporting Goods Association)

Solution
To sketch a scatter plot of the data shown in the table, you simply represent each pair of values by an ordered pair $(t, A)$ and plot the resulting points, as shown in Figure 4. For instance, the first pair of values is represented by the ordered pair $(1990,475)$. Note that the break in the $t$-axis indicates that the numbers between 0 and 1990 have been omitted.

Find the distance between the points $(-2,1)$ and $(3,4)$.

Algebraic Solution
Let $\left(x_1, y_1\right)=(-2,1)$ and $\left(x_2, y_2\right)=(3,4)$. Then apply the Distance Formula.
\begin{aligned} d & =\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2} & & \text { Distance Formula } \ & =\sqrt{[3-(-2)]^2+(4-1)^2} & & \begin{array}{l} \text { Substitute for } \ x_1, y_1, x_2 \text {, and } y_2 \text { – } \end{array} \ & =\sqrt{(5)^2+(3)^2} & & \text { Simplify. } \ & =\sqrt{34} & & \text { Simplify. } \ & \approx 5.83 & & \text { Usc a calculator. } \end{aligned}
So, the distance between the points is about 5.83 units. You can use the Pythagorean Theorem to check that the distance is correct.
\begin{aligned} d^2 & \stackrel{?}{=} 3^2+5^2 \ (\sqrt{34})^2 & \stackrel{?}{=} 3^2+5^2 \ 34 & =34 \end{aligned}
Pythagorean Theorem
Substitute for $d$.
Distance checks.

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