Find the Rate of Change in Linear Equation -8y+2x=6

To determine the rate of change for the given equation $-8y + 2x = 6$, follow these steps:

• Step 1: Rearrange the equation to isolate $y$. Start by subtracting $2x$ from both sides:
  $-8y = -2x + 6$.
• Step 2: Solve for $y$ by dividing every term by $-8$ to get $y$ by itself:
  $y = \frac{-2}{-8}x + \frac{6}{-8}$.
• Step 3: Simplify the fractions:
  $y = \frac{1}{4}x - \frac{3}{4}$.

In the equation $y = \frac{1}{4}x - \frac{3}{4}$, the coefficient of $x$ is $\frac{1}{4}$, which represents the rate of change (slope) of the line. Therefore, the rate of change is $\frac{1}{4}$.