3x + 4y = 12, solve for y
Understand the Problem
The question is asking us to solve the equation 3x + 4y = 12 for the variable y. We will isolate y on one side of the equation to find its expression in terms of x.
Answer
$$ y = 3 - \frac{3}{4}x $$
Answer for screen readers
The expression for y in terms of x is
$$ y = 3 - \frac{3}{4}x $$
Steps to Solve
- Isolate the term with y
To solve for y, we need to isolate it on one side of the equation. We start with the original equation:
$$ 3x + 4y = 12 $$
Next, we can subtract $3x$ from both sides:
$$ 4y = 12 - 3x $$
- Divide by the coefficient of y
Now we need to get y by itself. To do this, we divide both sides of the equation by 4:
$$ y = \frac{12 - 3x}{4} $$
- Simplify the expression
We can simplify further by splitting the fraction:
$$ y = \frac{12}{4} - \frac{3x}{4} $$
This simplifies to:
$$ y = 3 - \frac{3}{4}x $$
The expression for y in terms of x is
$$ y = 3 - \frac{3}{4}x $$
More Information
This final expression describes y as a linear function of x. It shows that for every increase in x, y decreases by $\frac{3}{4}$ of that increase. The equation represents a straight line with a slope of $-\frac{3}{4}$ and a y-intercept of 3.
Tips
- Forgetting to subtract $3x$ from both sides, leading to an incorrect measure of y.
- Miscalculating the division when isolating y, which can lead to inaccurate results.
