Question 618·Easy·Algebra

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$4x - 7 = 3y$

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

A linear equation that asks for $y$ in terms of $x$ is asking you to get $y$ alone. Graph the original equation in Desmos for a quick sign check, then divide by the number multiplying $y$ . The trap is dividing only the $x$ term: the constant term must be divided too.

Hints

Hint 1
To isolate $y$ means to get it alone on one side of the equation. Since a number multiplies $y$ , what number must you divide both sides by to undo that multiplication?
Hint 2
A fraction over a difference applies to both terms: $(a-b)/c=a/c-b/c$ . Once you divide the equation, what happens to the $4x$ term and the $-7$ term?

Step-by-step

Divide to isolate $y$
Step 1
Check the sign on the graph
Type $4x-7=3y$ in Desmos and click where its line crosses the $y$ -axis. Desmos shows approximately $(0,-2.333)$ . So when $x=0$ , $y$ is negative; your rewritten equation must keep a negative constant.
Step 2
Undo the multiplication by $3$
The given equation has $3y$ , so divide every term by the coefficient of $y$ . Divide both sides by $3$ :
$\frac{4x-7}{3}=y$
Step 3
Divide both terms in the numerator
The $3$ divides both $4x$ and $-7$ . Split the fraction and simplify each term:
$\frac{4x}{3}=\frac{4}{3}x,\qquad \frac{-7}{3}=-\frac{7}{3}$
Don't change the minus sign: no term crossed the equals sign.
Step 4
Check that the equations match
Put $y$ first and combine the terms. Type $y=\frac{4}{3}x-\frac{7}{3}$ below the original equation in Desmos. The lines overlap, so the new equation expresses the same relationship with $y$ alone. Choice D.

Question 618·Easy·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

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Strategy

Hints

Step-by-step

Lessons that teach this