Final answer:
The equation of the line that is perpendicular to y = -4x + 4 and passes through the point (-3, 2) is y = 1/4x + 11/4.
Step-by-step explanation:
The question involves finding the equation of a line that is perpendicular to a given line and passes through a specific point. The original line is given by the equation y = -4x + 4. To find a perpendicular line, we must use a slope that is the negative reciprocal of the original line's slope. Since the slope of the given line is -4, the slope of the perpendicular line will be 1/4. Using the point-slope form of a line's equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point, we plug in our values to get the equation of the perpendicular line.
Let's apply this to the given point (-3, 2):
- Perpendicular slope: m = 1/4
- Given point: (x1, y1) = (-3, 2)
- Point-slope form: y - 2 = 1/4(x + 3)
Now, simplify and put it in slope-intercept form (y = mx + b):
- y - 2 = 1/4x + 3/4
- y = 1/4x + 3/4 + 2
- y = 1/4x + 11/4
Therefore, the equation of the line perpendicular to the line y = -4x + 4 and passing through the point (-3, 2) is y = 1/4x + 11/4.