Put the following equation of a line into slope-intercept form, simplifying all fractions.

6, x, plus, 4, y, equals, 12

6*x*+4*y*=

12

To convert the equation \(6x + 4y = 12\) into **slope-intercept form** (\(y = mx + b\)), follow these steps:

### Step 1: Isolate the term with \(y\).
Subtract \(6x\) from both sides of the equation to move the \(x\) term to the right side:

\[
4y = -6x + 12
\]

### Step 2: Solve for \(y\).
Divide every term by 4 to isolate \(y\):

\[
y = \frac{-6x}{4} + \frac{12}{4}
\]

### Step 3: Simplify the fractions.
\[
y = \frac{-3x}{2} + 3
\]

So, the equation in slope-intercept form is:

\[
y = \frac{-3}{2}x + 3
\]

### Summary:
The slope-intercept form of the equation is \(y = \frac{-3}{2}x + 3\), where the slope \(m = \frac{-3}{2}\) and the y-intercept \(b = 3\).

Would you like more examples or help with graphing this equation?

### Relative Questions:
1. How do you interpret the slope \(\frac{-3}{2}\) in this equation?
2. What does the y-intercept of 3 mean in this line?
3. How would you graph this line on a coordinate plane?
4. What is the general process for converting equations to slope-intercept form?
5. How can you find the x-intercept from this equation?

**Tip**: In slope-intercept form, the slope tells you how steep the line is, while the y-intercept shows where the line crosses the y-axis.

Put the following equation of a line into slope-intercept form, simplifying all fractions: 6x + 4y = 12

Learn how to convert the equation 6x + 4y = 12 into slope-intercept form (y = mx + b) with simplified fractions. This guide covers key algebraic concepts like isolating y and simplifying terms, making it ideal for students in Grades 8-10.

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