The problem asks for the equation of a line passing through the point $(-4, -3)$ and having a slope of $-\frac{3}{4}$.

To find the equation of the line, we can use the point-slope form of the line equation:

$y - y_1 = m(x - x_1)$

Where:

• $m$ is the slope of the line.
• $(x_1, y_1)$ is the point the line passes through.

Here, the slope $m = -\frac{3}{4}$ and the point is $(-4, -3)$. Plugging in these values into the point-slope form:

$y - (-3) = -\frac{3}{4}(x - (-4))$

Simplifying:

$y + 3 = -\frac{3}{4}(x + 4)$

Now, distribute the slope $-\frac{3}{4}$:

$y + 3 = -\frac{3}{4}x - 3$

Finally, subtract 3 from both sides to get the equation in slope-intercept form:

$y = -\frac{3}{4}x - 6$

So, the equation of the line is:

$y = -\frac{3}{4}x - 6$

Would you like to dive deeper into any specific part of this process? Or do you have any further questions?

1. How can you convert a linear equation from point-slope form to slope-intercept form?
2. How do you calculate the slope of a line given two points?
3. What does the slope of a line represent in real-world situations?
4. What is the general form of the equation of a line, and how does it relate to the point-slope form?
5. Can you explain how to graph a line given its equation?

Tip: Always remember to simplify and check your final equation, ensuring it matches the slope and point given in the problem!