The independent variable *x* is hours, and the dependent variable *y* is pieces of candy left. Since the brother took 17 hours to eat 51 pieces of candy, he ate 51 ÷ 17 = 3 pieces of candy per hour. If we turn his candy-eating into an equation, we get *y* = 51 – 3*x*. If we turn that into slope-intercept form, we get *y* = -3*x *+ 51. The slope of this line is -3. The sister took 9 hours to eat 27 pieces of candy, so she was wolfing it down at a rate of 27 ÷ 9 = 3 pieces per hour. Her equation, then, is *y* = 27 – 3*x*, or *y* = -3*x* + 27 in slope-intercept form. That means we're trying to solve this system of equations: *y* = -3*x *+ 51
*y* = -3*x* + 27
Each line has a slope of -3. Since the lines are parallel, the system of linear equations they represent is inconsistent. The lines will never intersect, so the brother and sister will never have the same amount of candy. Until, of course, they're both left completely candy-less, at which point they simultaneously bust out into a good cry. |