Math  /  Algebra

Question(VCAA-type question) The rule connecting yy and xx as shown in the graph is: A y=2xy=2 x B y=2x2y=2 x^{2} c y=2xy=2 \sqrt{x} D y=12xy=\frac{1}{2} x E y=x2+2y=x^{2}+2

Studdy Solution

STEP 1

What is this asking? Which equation matches the straight line on the graph where the horizontal axis is x2x^2 and the vertical axis is yy? Watch out! The horizontal axis is x2x^2, not xx!
Don't get tricked!

STEP 2

1. Check the given point
2. Find the equation

STEP 3

Alright, let's **look** at the graph!
We've got a straight line, and it goes through the point (2,42, 4).
Remember, the horizontal axis is x2x^2, so at this point, x2=2x^2 = 2 and y=4y = 4.

STEP 4

Since the graph is a straight line, the relationship between yy and x2x^2 must be linear.
We can write this general relationship as y=mx2y = m \cdot x^2, where mm is the **slope** of the line.

STEP 5

We know that when x2=2x^2 = 2, y=4y = 4.
Let's **plug** these values into our equation: 4=m24 = m \cdot 2

STEP 6

To **solve** for mm, we can divide both sides of the equation by 22: 42=m22\frac{4}{2} = \frac{m \cdot 2}{2} 2=m2 = m

STEP 7

So, our **slope** is 22!
That means the equation of the line is y=2x2y = 2 \cdot x^2, or y=2x2y = 2x^2.

STEP 8

The correct answer is B, y=2x2y = 2x^2.

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