To find the x- and y-intercepts of the equation $1 - 6y = -23 - 8x$, we need to follow these steps:

1. Find the y-intercept:

The y-intercept occurs when $x = 0$. Substitute $x = 0$ into the equation:

$1 - 6y = -23 - 8(0)$ $1 - 6y = -23$ Now solve for $y$:

$-6y = -23 - 1$ $-6y = -24$ $y = \frac{-24}{-6} = 4$

Thus, the y-intercept is $(0, 4)$.

2. Find the x-intercept:

The x-intercept occurs when $y = 0$. Substitute $y = 0$ into the equation:

$1 - 6(0) = -23 - 8x$ $1 = -23 - 8x$ Now solve for $x$:

$8x = -23 - 1$ $8x = -24$ $x = \frac{-24}{8} = -3$

Thus, the x-intercept is $(-3, 0)$.

Final Answer:

• x-intercept: $(-3, 0)$
• y-intercept: $(0, 4)$

Would you like further details or have any questions?

Here are 5 related questions:

1. How do you graph these intercepts on a coordinate plane?
2. What does finding intercepts tell us about the behavior of a line?
3. Can you rewrite the equation in slope-intercept form?
4. How would you find the slope of this line?
5. How would the intercepts change if the equation was altered?

Tip: Always check if setting $x$ or $y$ to zero simplifies solving for intercepts!