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

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

Where:

• $(x_1, y_1)$ is a point on the line (in this case, $(4, -2)$),
• $m$ is the slope (in this case, $-\frac{3}{4}$).

Substituting the given values into the formula:

$y - (-2) = -\frac{3}{4}(x - 4)$

Simplify:

$y + 2 = -\frac{3}{4}(x - 4)$

Distribute the slope on the right-hand side:

$y + 2 = -\frac{3}{4}x + 3$

Now subtract 2 from both sides to isolate $y$:

$y = -\frac{3}{4}x + 3 - 2$

$y = -\frac{3}{4}x + 1$

Thus, the equation of the line is:

$y = -\frac{3}{4}x + 1$

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you convert point-slope form to slope-intercept form?
2. What is the general formula for a linear equation?
3. How can you find the slope between two points?
4. How would the equation change if the slope were positive?
5. What does the slope of a line represent in real-world problems?

Tip: The slope tells you how steep a line is and the direction it goes. Negative slopes mean the line decreases as $x$ increases.