To find the slope of the line given by the equation $y = -4x - \frac{7}{4}$, we can compare it with the slope-intercept form of a linear equation, which is:

$y = mx + b$

Here, $m$ represents the slope of the line, and $b$ is the y-intercept.

In the equation $y = -4x - \frac{7}{4}$:

• The coefficient of $x$ is $-4$, which means the slope $m$ is $-4$.

So, the slope of the line is $\boxed{-4}$.

Would you like more details or have any questions?

Here are five related questions to expand your understanding:

1. How do you find the y-intercept from the equation $y = -4x - \frac{7}{4}$?
2. What is the slope of the line $y = 3x + 2$?
3. If two lines have the same slope, what can you say about their relationship?
4. How would the slope change if the equation was $y = 4x - \frac{7}{4}$?
5. What is the slope of a line parallel to $y = -4x - \frac{7}{4}$?

Tip: The slope is a measure of the steepness of a line. A negative slope indicates the line is decreasing, while a positive slope indicates the line is increasing.