You are traveling away from home at a constant speed. After 3 hours you are 60 miles from home and hours you are 160 miles from home. Write an equation that models $y$, your distance (in miles) from home after $x$ hours.

Step 1 ：Given two points (3, 60) and (6, 160) on the line, we can calculate the slope of the line using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\).

Step 2 ：Substitute the given points into the formula to get \(m = \frac{160 - 60}{6 - 3} = 33.33\). So, the slope of the equation, which represents the speed at which you are traveling, is approximately 33.33 miles per hour.

Step 3 ：The y-intercept is the value of y when x = 0. This can be found by substituting the slope and one of the points into the equation and solving for b. We get \(b = y - mx = 60 - 33.33 \times 3 = -40\).

Step 4 ：However, the y-intercept is -40, which means that at time 0, the distance from home would be -40 miles. This doesn't make sense in the context of the problem, as you can't be a negative distance from home. This discrepancy is due to the fact that the speed was not constant for the first 3 hours.

Step 5 ：Therefore, the equation that models the distance from home after x hours is \(y = 33.33x - 40\).

Step 6 ：\(\boxed{y = 33.33x - 40}\) is the final answer.