To find the perpendicular line to y = -4x - 2 passing through (4, -4), calculate the negative reciprocal slope of 1/4 and use the point-slope form to derive the new line's equation, which is y = (1/4)x - 5.
To find the equation of the line perpendicular to y = -4x - 2 that passes through the point (4, -4), we must identify the slope of the given line and use the fact that the slopes of perpendicular lines are negative reciprocals of each other. The given line has a slope of -4. The slope of the perpendicular line will then be the negative reciprocal, which is 1/4.
Using this slope and the point (4, -4), we can apply the point-slope form: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through. Let's substitute the values into this equation:
y + 4 = (1/4)(x - 4)
Simplify to get the equation in slope-intercept form (y = mx + b):
y + 4 = (1/4)x - 1
Subtract 4 from both sides:
y = (1/4)x - 5
This is the equation of the line perpendicular to y = -4x - 2 passing through the point (4, -4) in slope-intercept form.