Final answer:
The correct equation to represent the trip where x is the number of hours and y is the number of miles left is y = 14 - 2x. This linear equation can be graphed with a y-intercept at (0,14) and a slope of -2.
Step-by-step explanation:
The scenario describes a woman who takes 1 hour to complete 2 miles of her trip, with a total trip distance of 14 miles. The equation that represents the number of miles she has left compared to the number of hours she is out would be y = 14 - 2x. Here, x represents the number of hours she is out, and y represents the number of miles she has left to travel until she is back home. Since she completes 2 miles per hour, for each hour that goes by, the number of miles left decreases by 2. Starting with 14 miles, after x hours, she will have 14 - 2x miles left. Therefore, the correct equation is option A: y = 14 - 2x.
To graph this equation, you would plot the y-intercept at (0,14) and use a slope of -2 to determine additional points on the line. For instance, after 1 hour (x = 1), she would have 12 miles left (y = 14 - 2 * 1 = 12). After 2 hours (x = 2), she would have 10 miles left (y = 14 - 2 * 2 = 10), and so on until the graph intersects the x-axis at x = 7, meaning she has completed her trip and has 0 miles left to travel.