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Solve for x: 3x + 4y = 7

A. y = 3x + 7
B. y = -3/4x + 7
C. -3/4x + 7/4

1 answer

To solve for \( y \) in terms of \( x \) from the equation \( 3x + 4y = 7 \), we will isolate \( y \).

  1. Start with the original equation:

    \[ 3x + 4y = 7 \]

  2. Subtract \( 3x \) from both sides:

    \[ 4y = 7 - 3x \]

  3. Now, divide both sides by 4:

    \[ y = \frac{7 - 3x}{4} \]

  4. We can rewrite this as:

    \[ y = -\frac{3}{4}x + \frac{7}{4} \]

Now, let's examine the options:

A. \( y = 3x + 7 \) - This is incorrect.

B. \( y = -\frac{3}{4}x + 7 \) - This is incorrect because the constant term should be \( \frac{7}{4} \).

C. \( y = -\frac{3}{4}x + \frac{7}{4} \) - This is correct.

So the solution for \( y \) in terms of \( x \) is:

\[ \boxed{C} \]