Final answer:
The equation for the line parallel to y = -4x + 3 that passes through (1, -2) is y = -4x + 2, as it has the same slope of -4 and the y-intercept is calculated using the point-slope equation.
Step-by-step explanation:
The student's question is asking for the equation of a line that is parallel to a given line and passes through a specified point. The given line is y = −4x + 3, which means any line parallel to it must have the same slope, which is -4. To find the y-intercept (b) of the new line passing through the point (1,−2), we use the point-slope form of a linear equation y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope. Plugging in the values, we get y - (-2) = -4(x - 1), which simplifies to y = -4x + 2, so the correct answer is B) y = -4x + 2.