Final answer:
The equation of the line in slope-intercept form that is perpendicular to y = -4x - 2 and passes through the point (4, -4) is y = 1/4x - 5.
Step-by-step explanation:
The subject of this question is Mathematics, specifically the algebra of straight lines within High School level coursework. To find the equation of a line in slope-intercept form that is perpendicular to another line, we first need to determine the slope of the original line, and then find the negative reciprocal of that slope for the perpendicular line. The given line is y = -4x - 2, which means its slope is -4. The slope of a line perpendicular to this would be the negative reciprocal, which is 1/4.
Now, using the point (4, -4) that the new line must pass through, we can substitute into the slope-intercept form of the equation, which is y = mx + b, where m is the slope and b is the y-intercept. Plugging in the point and the slope, we get -4 = (1/4)*4 + b, which simplifies to -4 = 1 + b. Solving for b gives us b = -5, hence the equation for the new line is y = 1/4x - 5.