Final answer:
The equation of line B, which is perpendicular to line A with an equation of y = -x - 4 and passes through the point (-2, 1), is y = x + 3.
Step-by-step explanation:
The equation for line A is y = -x - 4. Since line A and line B are perpendicular, line B will have a slope that is the negative reciprocal of the slope of line A. The slope of line A is -1, so the slope of line B will be 1 (the negative reciprocal of -1). Furthermore, line B passes through the point (-2, 1). Using the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept, we can plug in the slope of line B and the coordinates of the point it passes through to find the equation of line B.
To find the y-intercept (b), we use the formula y = mx + b, where x and y are the coordinates of the point (-2, 1) and m is the slope of line B (which is 1). This gives us the equation 1 = (1)(-2) + b, which simplifies to 1 = -2 + b. Solving for b gives us b = 3. Therefore, the equation of line B, which is perpendicular to line A and passes through the point (-2, 1), is y = x + 3.