The equation of a line in point-slope form is:

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

where:

• $m = -2$ (the given slope),
• $(x_1, y_1) = (4, -8)$ (the given point).

Step 1: Substitute the values

$y - (-8) = -2(x - 4)$

$y + 8 = -2(x - 4)$

Step 2: Distribute the slope

$y + 8 = -2x + 8$

Step 3: Solve for $y$ (convert to slope-intercept form)

$y = -2x + 8 - 8$

$y = -2x$

Final Answer:

$y = -2x$

This is the equation of the line in slope-intercept form ($y = mx + b$).

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Would you like a detailed explanation of how I distributed and simplified the equation?

Related Questions:

1. How do you convert an equation from point-slope form to standard form?
2. What is the general formula for a line given two points?
3. How do you find the equation of a perpendicular line to this one passing through a given point?
4. How do you determine if a point lies on this line?
5. What is the x-intercept of this line?

Tip: When given a point and a slope, always start with the point-slope formula for quick calculations!