Final answer:
The equation of the line perpendicular to y + 1 = -\(\frac{1}{2}\)x that passes through (−8, 7) is y = 2x + 23.
Step-by-step explanation:
To find the equation of a line perpendicular to y + 1 = -\(\frac{1}{2}\)x that passes through the point (-8, 7), we first identify the slope of the given line. The slope of the given line is -\(\frac{1}{2}\). Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of the line we are seeking is 2.
Next, we use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Substituting the slope 2 and the point (-8, 7) into the point-slope form gives us y - 7 = 2(x + 8).
Finally, we simplify the equation to put it into slope-intercept form, yielding y = 2x + 23. This is the equation of the line that is perpendicular to y + 1 = -\(\frac{1}{2}\)x and passes through the point (-8, 7).