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Answer 1

We have the equation for company 1: y = 3x + 5.  That means it costs $3 to rent a movie with a $5 fee no matter how many movies you rent.  It would benefit us to have the equation for company 2, so we need to find it using 2 points on the line.  I picked the points (2,14) and (0,12).  Find the slope of this by using the slope formula: $m= \frac{12-14}{0-2}$ which gives us a slope of 1.  Now we can use that slope and the slope-intercept form of a line to find the y-intercept, which serves as the fee for renting from company 2. 14=1(2)+b and 14 = 2 + b and b = 12.  The equation then for company 2 is y=1x+12.  This means it costs $1 to rent movies, but your fee to rent, no matter how many movies you pick, is $12.  The "rate of change" in the choices refers to the slope.  The slope in company 1's equation is 3 and the slope in company 2's equation is 1.  The best description is the first choice that says "There is a higher rate of change at Company 1".