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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.

Find the equation of the line in slope-intercept form that passes through the point (0, -4) with the slope of -3.

Learn how to find the equation of a line in slope-intercept form that passes through the point (0, -4) with a slope of -3. This problem explains key algebraic concepts such as linear equations and slope-intercept form. Suitable for students in Grades 7-9.

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