Question 115·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

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x^2 + y = 9

The equation relates the variables $x$ and $y$ . Which equation correctly expresses $y$ in terms of $x$ ?

The phrase “express $y$ in terms of $x$ ” signals a formula rearrangement: get $y$ alone while leaving $x$ in the result. Desmos can show a point that helps you check the sign of your answer. Then subtract the term beside $y$ from both sides. Moving that term without changing its sign gives the wrong formula.

Hints

Hint 1
To express $y$ in terms of $x$ , $y$ must stand alone; $x$ can remain in the answer. What term is added to $y$ on the left side of the equation?
Hint 2
Use the balance rule: do the same operation to both sides. Subtracting the term beside $y$ will remove it from the left. What remains on the right?

Step-by-step

Subtract to isolate $y$
Step 1
Check the starting value
Type $x^2+y=9$ in Desmos and click the top of the curve. Desmos labels it $(0,9)$ . This is the $y$ -intercept, the point where $x=0$ , so the correct formula must give $y=9$ when $x=0$ .
Step 2
Get $y$ alone
The question asks for $y$ in terms of $x$ , so leave $x$ in the answer. To keep an equation balanced, do the same operation to both sides. Subtract $x^2$ from both sides:
$x^2+y-x^2=9-x^2$
Cancel $x^2-x^2$ on the left:
$y=9-x^2$
This expresses $y$ in terms of $x$ and gives $9$ when $x=0$ . Choice D.

Lessons that teach this

SAT Advanced AlgebraIntermediateCoreRearrange nonlinear formulas

Question 115·Easy·Nonlinear Equations in One Variable; Systems in Two Variables

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this