To find the equation of the line in slope-intercept form $y = mx + b$ that passes through the point $(-4, -8)$ and is parallel to the line given by $y = -6x - 7$, follow these steps:

Step 1: Identify the slope of the given line

The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope. The slope of the given equation $y = -6x - 7$ is $m = -6$.

Since the new line is parallel to this line, it will have the same slope. Thus, the slope of the new line is also $-6$.

Step 2: Use the point-slope form to find the equation

We can use the point-slope form of the equation of a line, which is: $y - y_1 = m(x - x_1)$ Where $m$ is the slope, and $(x_1, y_1)$ is the given point. Substituting $m = -6$ and $(x_1, y_1) = (-4, -8)$, we get: $y - (-8) = -6(x - (-4))$ This simplifies to: $y + 8 = -6(x + 4)$

Step 3: Simplify to slope-intercept form

Now, simplify the equation to put it in the form $y = mx + b$: $y + 8 = -6x - 24$ Subtract 8 from both sides: $y = -6x - 24 - 8$ $y = -6x - 32$

Final Equation:

The equation of the line in slope-intercept form is: $y = -6x - 32$

Would you like further details or have any questions?

Here are 5 related questions to explore:

1. How do you find the slope of a line from two points?
2. What happens when two lines are perpendicular instead of parallel?
3. How would the equation change if the line passed through a different point?
4. How do you convert from point-slope form to slope-intercept form?
5. How do you determine the y-intercept of a line?

Tip: When two lines are parallel, they always have the same slope, no matter their y-intercepts.