Final answer:
The slope-intercept form of the line parallel to y = -4x + 2 and passing through (-2, 2) is y = -4x - 6.
Step-by-step explanation:
To find the slope-intercept form of the line that passes through the point (-2, 2) and is parallel to the line y = -4x + 2, we will use the concept that parallel lines have the same slope. Since the slope of the given line is -4 (m=-4), the line we are seeking will also have a slope of -4. The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
To find the y-intercept (b) of our line, we will use the point (-2, 2) that the line must pass through. Substituting in the slope (m=-4) and this point into the equation gives us:
2 = (-4)(-2) + b
Which simplifies to:
2 = 8 + b
Subtracting 8 from both sides we get:
b = -6
Thus, the equation of our line is y = -4x - 6.