Put the following equation of a line into slope-intercept form, simplifying all fractions.
4, y, minus, 2, x, equals, minus, 8
4y−2x=
−8

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!

Put the following equation of a line into slope-intercept form, simplifying all fractions: 4y - 2x = -8

Learn how to convert the linear equation 4y - 2x = -8 into slope-intercept form (y = mx + b) with a simplified step-by-step solution. This problem demonstrates key algebraic concepts, including isolating y, simplifying fractions, and identifying slope and y-intercept. Suitable for students in Grades 7-9.

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