To find the equation of the line passing through the point $(4, -2)$ with a slope of $-\frac{3}{4}$, you can use the point-slope form of the equation of a line:

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

Where:

• $m$ is the slope of the line
• $(x_1, y_1)$ is a point on the line

Substitute the given point $(4, -2)$ and the slope $-\frac{3}{4}$ into the equation:

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

Simplify the equation:

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

Distribute the slope $-\frac{3}{4}$ to both terms inside the parentheses:

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

Now, isolate $y$ by subtracting 2 from both sides:

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

Simplify further:

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

So, the equation of the line is:

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

Would you like more details or have any other questions?

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Here are 5 related questions:

1. How do you find the y-intercept of a line given its equation?
2. What is the equation of a line parallel to this one and passing through a different point?
3. How can you determine if two lines are perpendicular?
4. How would the equation change if the slope was positive?
5. What is the distance from the origin to this line?

Tip: Always double-check your calculations when substituting values into equations to avoid small mistakes.