Math  /  Algebra

Question(4) Whice the can 5) Decide whether each of the following is a linear refation or not. Explain how vou know in each case. a) A number is ahisily ? more than the square of another number

Studdy Solution

STEP 1

What is this asking? Is the relationship, "one number is always 2 more than the square of another number," a linear relationship? Watch out! Squaring a variable is a classic sign of a non-linear relationship!
Don't be fooled!

STEP 2

1. Express the relationship as an equation.
2. Analyze the equation.

STEP 3

Let yy be "one number" and xx be "another number."

STEP 4

The phrase "a number is always **2 more than**" translates to adding **2**.
The phrase "the **square** of another number" means we're going to have an x2x^2.
So, our equation is y=x2+2y = x^2 + 2.

STEP 5

The equation y=x2+2y = x^2 + 2 includes a **squared term**, x2x^2.

STEP 6

Linear equations have the general form y=mx+by = mx + b, where mm is the **slope** and bb is the y-intercept\textbf{y-intercept}.
Notice how the variable xx is *not* raised to any power other than 1.

STEP 7

Our equation, y=x2+2y = x^2 + 2, has an x2x^2 term.
This makes it *different* from the structure of a linear equation.

STEP 8

No, the relationship "a number is always 2 more than the square of another number" is *not* a linear relationship.
The presence of the x2x^2 term makes it a **quadratic relationship**, not a linear one.

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