To find the equation of the line that passes through the point $(-4, 1)$ and has a slope of $-\frac{5}{4}$, we can use the point-slope form of the equation of a line, which is:

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

Here:

• $m = -\frac{5}{4}$ (the slope),
• $(x_1, y_1) = (-4, 1)$ (the point the line passes through).

Substituting these values into the point-slope form:

$y - 1 = -\frac{5}{4}(x + 4)$

Now, let's simplify this equation step by step:

1. Distribute the slope $-\frac{5}{4}$ on the right-hand side:

$y - 1 = -\frac{5}{4}x - \frac{5}{4} \times 4$

2. Simplify the multiplication:

$y - 1 = -\frac{5}{4}x - 5$

3. Finally, add 1 to both sides to get the equation in slope-intercept form $y = mx + b$:

$y = -\frac{5}{4}x - 4$

So, the equation of the line is:

$y = -\frac{5}{4}x - 4$

Would you like more details or have any questions?

Related Questions:

1. How do you convert a linear equation to standard form?
2. What is the general formula for finding the equation of a line given two points?
3. How do you find the slope of a line given two points?
4. What does the slope of a line represent geometrically?
5. How can you determine if two lines are parallel or perpendicular using their slopes?

Tip:

When working with linear equations, it's often helpful to graph the line to visually verify that it passes through the given point and has the correct slope.