To write the equation of a line with a given slope $m = 4$ that passes through the point $(0, -3)$, we can use the point-slope form of a line:

$y = mx + b$

where:

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

Since the line passes through $(0, -3)$, the y-intercept $b$ is $-3$. Substituting the values of $m$ and $b$ into the equation gives:

$y = 4x - 3$

Thus, the equation of the line is:

$y = 4x - 3$

Would you like additional details or have any questions?

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Here are some related questions for further exploration:

1. What would the equation be if the slope was changed to $-4$?
2. How do you find the equation of a line passing through two points?
3. What are the steps to convert this line equation into standard form?
4. How would the graph of this equation look compared to a line with slope $4$ and y-intercept $0$?
5. How can we verify that the point $(0, -3)$ lies on the line?

Tip: To determine if a point lies on a line, substitute the point's coordinates into the line's equation and check if it holds true.