Question

rate of growth 37 cm 22 cm 0.75 cm per year 1.5 cm per year mayra wrote two equations to represent the length of a shark, y, and x years of growth. when she graphed the equations on the desmos graphing calculator, as shown below, the lines intersected at (20, 52). y = 37 + 0.75x y = 22 + 1.5x what does this point mean in relationship to the scenario above? after 20 years, the rates of growth are the same for both sharks. after 20 years, the sharks have increased in length by 52 cm. after 52 years, the sharks have both grown by 20 cm. after 20 years, the sharks are both 52 cm in length.

Explanation:

In the context of the equations \(y = 37+0.75x\) (where \(37\) is the initial length and \(0.75\) is the growth rate per year) and \(y = 22 + 1.5x\) (where \(22\) is the initial length and \(1.5\) is the growth rate per year), the point of intersection \((x,y)=(20,52)\) of the two lines in a system of linear equations means that when \(x = 20\) (years of growth), the value of \(y\) (length of the shark) is the same for both equations. The \(x\) - value represents the number of years, and the \(y\) - value represents the length of the shark. The growth rates (\(0.75\) and \(1.5\) cm per year) are constants in the equations and do not change at \(x = 20\). The \(y\) - value is the total length, not just the increase (since the initial lengths \(37\) and \(22\) are added to the growth terms).

Answer:

After 20 years, the sharks are both 52 cm in length.