To convert the given equation $6x + 4y = 16$ into slope-intercept form $y = mx + b$, follow these steps:

Step 1: Isolate the $y$-term.

Start with the original equation: $6x + 4y = 16$ Subtract $6x$ from both sides to get the $y$-term alone on one side: $4y = -6x + 16$

Step 2: Solve for $y$.

Now, divide each term by 4 to isolate $y$: $y = \frac{-6x}{4} + \frac{16}{4}$ Simplify the fractions: $y = -\frac{3}{2}x + 4$

So, the equation in slope-intercept form is: $y = -\frac{3}{2}x + 4$

Final Answer:

The equation in slope-intercept form is $y = -\frac{3}{2}x + 4$.

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Would you like to explore more details about slope-intercept form or need further help with other types of problems? Here are a few related questions you can explore:

1. How do you identify the slope and y-intercept from a given equation?
2. What is the general formula for the slope of a line given two points?
3. How do you graph a line from its slope-intercept form equation?
4. What does the slope of a line represent in real-world situations?
5. How would the equation change if the y-intercept were negative?

Tip: Always ensure the fractions are simplified to their lowest terms to make the slope and y-intercept easy to work with.