By reading a graph describing a country's defense spending, you discover that in 1985 the country spent $\$ 84$ million on defense and in 1993 spent $\$ 420$ million. Let $x=0$ represent 1985 and $x=8$ represent 1993. Write a linear function that relates $y$ (in millions of dollars) to $x$. Use slope-intercept form. A. $y=-42 x-84$ B. $y=63 x+84$ C. $y=42 x+84$ D. $y=\frac{1}{2} x+84$

Step 1 ：The problem is asking for a linear function in the form of \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. The slope can be calculated using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\), where \((x_1, y_1)\) and \((x_2, y_2)\) are two points on the line. In this case, the two points are \((0, 84)\) and \((8, 420)\). The y-intercept \(b\) is the value of \(y\) when \(x = 0\), which is given as \(84\).

Step 2 ：Calculate the slope \(m\) using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\) = \frac{420 - 84}{8 - 0} = 42.

Step 3 ：The slope of the line is 42 and the y-intercept is 84. Therefore, the linear function that relates y (in millions of dollars) to x is \(y = 42x + 84\).

Step 4 ：Final Answer: \(\boxed{y = 42x + 84}\)