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.