Final answer:
To find the equation of a line that is perpendicular to y = -(1/2)x + 3 and passes through (-5, -4), the slope is determined to be 2, and by using the point-slope form, the equation of the perpendicular line is y = 2x + 6.
Step-by-step explanation:
The student is asking for help in determining the equation of a line that passes through the point (-5, -4) and is perpendicular to a given line with the equation y = -(1/2)x + 3. To find the equation of the perpendicular line, one must first understand that the slopes of perpendicular lines are negative reciprocals of each other.
Therefore, if the given line has a slope of -(1/2), the perpendicular line will have a slope of 2 because -1/(-1/2) equals 2. Using this new slope and the point (-5, -4), we can apply the point-slope form of a line which is y - y1 = m(x - x1). Substituting the known values gives us y - (-4) = 2(x - (-5)). Simplifying further, we get y + 4 = 2x + 10, and then y = 2x + 6 as the final equation of the line perpendicular to the given line and passing through (-5, -4).