The distance that Marisol and Mimi covers depends on how many hours they walk. Therefore, the time in hours x is the independent variable, and the distance in miles y is the dependent variable.
Since the two girls walk at a constant rate, the distance they cover can be represented by linear equations in slope-intercept form.
y=mx+b
In this equation, m is the line's slope and b is the y-intercept. To draw the graphs, we need at least two points through which each graph passes. From the exercise, we know that Marisol starts walking at x=0, while Mimi starts one hour later at x=1. This can be translated to the data points (0,0) and (1,0), respectively.
From the exercise we also know that Marisol walks 2 miles per hour, while Mimi walks 3 miles per hour. With this information, we can find a second point through which each graph passes and draw the function's graphs.
To finalize the equations that describe Mimi's walk, we have to substitute one of the known points into the equation and solve for b.
If they reach the mall at the same time they have traveled the same distance, which is represented graphically as the intersection point between the two graphs. We can find the time when this occurs by equating the right-hand sides of the equations and solving for x.
They meet after 3 hours. By substituting this value into either equation, we can find the distance they have walked and therefore how far from the mall their school is.
