Question

1. tek a.2b which of the following is equivalent to $3x - 4y = 6$?

options:
$y = -\frac{3}{4}x$
$y = \frac{4}{3}x + 2$
$y = \frac{3}{4}x - \frac{3}{2}$
$y = -\frac{6}{7}x$

Explanation:

Step1: Isolate the y - term

We start with the equation \(3x - 4y=6\). Subtract \(3x\) from both sides of the equation.
\(3x-4y - 3x=6 - 3x\)
Simplifying the left - hand side, we get \(- 4y=6 - 3x\)

Step2: Solve for y

Divide every term in the equation \(-4y = 6-3x\) by \(-4\).
\(y=\frac{6}{-4}-\frac{3x}{-4}\)
Simplify each fraction: \(\frac{6}{-4}=-\frac{3}{2}\) and \(\frac{- 3x}{-4}=\frac{3}{4}x\)
So, \(y = \frac{3}{4}x-\frac{3}{2}\)

Answer:

\(y=\frac{3}{4}x-\frac{3}{2}\) (the second option from the left among the given options)