Let's break this down step by step.

You gave the equation:

$-8y = -48$

Step 1: Solve for $y$

First, let's isolate $y$ in the equation:

$-8y = -48$

To solve for $y$, divide both sides by $-8$:

$y = \frac{-48}{-8} = 6$

So, the value of $y$ is 6.

Finding the intercepts

1. $y$-intercept: The $y$-intercept is the value of $y$ when $x = 0$. In this case, the equation only has $y$, and no $x$-term is present, meaning there is no $x$-intercept for this equation. So, the $y$-intercept is $y = 6$.

2. $x$-intercept: For the $x$-intercept, we typically set $y = 0$ and solve for $x$. But since this equation has no $x$-term, it doesn't intersect the x-axis (i.e., there is no $x$-intercept). The equation is simply a horizontal line at $y = 6$.

Conclusion:

• $y$-intercept: $(0, 6)$
• $x$-intercept: Does not exist (horizontal line)

Let me know if you need further clarification on this or if you have additional questions!

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Related Questions:

1. How do you find the intercepts of a linear equation with both $x$ and $y$?
2. What is the slope of a horizontal line?
3. What is the general form of a linear equation?
4. How do you determine the slope from an equation in standard form?
5. Can a linear equation have multiple intercepts?

Tip: For horizontal lines, the equation will always be of the form $y = \text{constant}$, and it will never have an $x$-intercept because the line never crosses the x-axis.