We are asked to find the equation of a line in slope-intercept form $y = mx + b$ that passes through the point $(0, -4)$ with a given slope $m = -3$.

The slope-intercept form is: $y = mx + b$ Where:

• $m$ is the slope,
• $b$ is the y-intercept.

Since the point $(0, -4)$ is given, this means when $x = 0$, $y = -4$. In the slope-intercept form, the value of $y$ when $x = 0$ gives the y-intercept, which is $b$. So, $b = -4$.

Now, we can substitute the values of $m = -3$ and $b = -4$ into the equation: $y = -3x - 4$

Thus, the equation of the line is: $y = -3x - 4$

Would you like more details or clarifications?

Here are 5 related questions you can explore:

1. How do you find the equation of a line given two points?
2. What happens to the equation of a line if the slope is zero?
3. How do you convert from slope-intercept form to standard form?
4. What is the significance of the y-intercept in a graph?
5. How do parallel lines relate in terms of their slopes?

Tip: When identifying the slope of a line, remember that a negative slope means the line goes downwards as you move from left to right.