To put the given equation $4y - 2x = -8$ into slope-intercept form $y = mx + b$, follow these steps:

Step 1: Isolate the $y$-term

Add $2x$ to both sides of the equation to move the $x$-term to the right-hand side: $4y = 2x - 8$

Step 2: Solve for $y$

Divide both sides of the equation by 4 to isolate $y$: $y = \frac{2x - 8}{4}$

Step 3: Simplify the fraction

Now, simplify the terms on the right-hand side: $y = \frac{2x}{4} - \frac{8}{4}$ $y = \frac{1}{2}x - 2$

Final equation

The equation of the line in slope-intercept form is: $y = \frac{1}{2}x - 2$

In this form, the slope $m = \frac{1}{2}$ and the y-intercept $b = -2$.

Would you like further details or have any questions?

Related Questions:

1. What does the slope $m = \frac{1}{2}$ represent in the context of this line?
2. How do you find the x- and y-intercepts of a line from its slope-intercept form?
3. How can you verify that this line is equivalent to the original equation?
4. What is the general process for converting any linear equation to slope-intercept form?
5. How do you graph a line using its slope and y-intercept?

Tip:

When simplifying fractions, divide each term of the numerator by the denominator separately to avoid errors!