Question 528·Easy·Algebra

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4y - 3x = 12

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

To express $y$ in terms of $x$ , isolate $y$ : get it alone on one side of the equation. Graph the given line in Desmos for a quick check, then undo the $x$ -term and divide by the number multiplying $y$ . Watch the sign of the $x$ -term when you move it.

Hints

Hint 1
The y-intercept is where the line crosses the vertical axis, so $x=0$ there. Graph the given equation and read that point. What value must your finished expression give when $x=0$ ?
Hint 2
To isolate $y$ means to get $y$ alone. The equation has $-3x$ beside $4y$ , so use the opposite operation: add $3x$ to both sides.
Hint 3
The coefficient of $y$ is the number multiplying it. Once you have $4y$ alone, divide both sides by $4$ . Keep the entire expression on the other side together.

Step-by-step

Graph to check, then isolate $y$
Step 1
Get a sign check from the graph
Type $4y-3x=12$ in Desmos and click where the line crosses the vertical axis. Desmos shows $(0,3)$ , and the line rises as $x$ increases. So your answer must give $y=3$ when $x=0$ and must rise with $x$ . That crossing is called the y-intercept.
Step 2
Move the $x$ -term away from $y$
An inverse operation undoes an operation. Add $3x$ to both sides to cancel $-3x$ :
$4y-3x+3x=12+3x$ $4y=3x+12$
The $x$ -term is now positive, matching the line's rise.
Step 3
Get $y$ alone
Divide both sides by $4$ , the number multiplying $y$ :
$\frac{4y}{4}=\frac{3x+12}{4}$ $y=\frac{3x+12}{4}$
This gives $3$ when $x=0$ and expresses $y$ in terms of $x$ . Choice D.

Question 528·Easy·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this