Let's solve this step by step.

Step 1: Convert the equation to slope-intercept form (y = mx + b)

We are given the equation: $3x + 4y = 12$

To convert it to slope-intercept form (which is $y = mx + b$), solve for $y$:

$4y = -3x + 12 \quad \text{(subtract } 3x \text{ from both sides)}$ $y = \frac{-3}{4}x + 3 \quad \text{(divide everything by 4)}$

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

Step 2: Identify the X-intercept and Y-intercept

X-intercept:

The X-intercept occurs when $y = 0$. Substitute $y = 0$ into the equation: $0 = \frac{-3}{4}x + 3$ Solve for $x$: $\frac{-3}{4}x = -3$ $x = 4$ Thus, the X-intercept is $x = 4$, or the point $(4, 0)$.

Y-intercept:

The Y-intercept occurs when $x = 0$. Substitute $x = 0$ into the equation: $y = \frac{-3}{4}(0) + 3 = 3$ Thus, the Y-intercept is $y = 3$, or the point $(0, 3)$.

Summary:

• Equation in slope-intercept form: $y = \frac{-3}{4}x + 3$
• X-intercept: $4$
• Y-intercept: $3$

Would you like more details on this process or to ask any follow-up questions?

Here are 5 related questions:

1. How do you find the slope from a linear equation?
2. Can we find the slope without converting to slope-intercept form?
3. What does the slope represent in a real-world context?
4. How do the X and Y intercepts help in graphing a line?
5. How can we verify the intercepts using a different method?

Tip: The slope tells you how much $y$ changes for every unit increase in $x$.