The value of y varies directly as the square of x and y = 2 when x = 2. What is y when x = 7?

y = 24.5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS Equality Properties

Algebra I

Directly Varies: y = kxInversely Varies: yx = k

Step-by-step explanation:

Step 1: Define

Varies directly: y = kx²

y = 2

x = 2

Step 2: Solve for k

Isolate k:                    k = y/x²Substitute:                 k = 2/2²Evaluate:                    k = 2/4Simplify:                     k = 1/2

Step 3: Find y

k = 1/2

x = 7

y = ?

Define:                          y = kx²Substitute:                    y = 1/2 · (7)²Evaluate:                       y = 1/2(49)Multiply:                        y = 49/2Divide:                          y = 24.5