Final answer:
The slope of the perpendicular line is the negative reciprocal of 1/2, which is -2. Using the point-slope form of a line, the equation is y - 4 = -2(x + 3).
Step-by-step explanation:
To find the equation of a line perpendicular to y = 1/2x + 3 passing through the point (-3,4), we need to determine the slope of the given line.
The slope-intercept form of a line is y = mx + b, where m represents the slope and b represents the y-intercept.
In this case, the slope of the given line is 1/2.
Since the line we want is perpendicular to the given line, its slope will be the negative reciprocal of 1/2.
The negative reciprocal of 1/2 is -2.
Therefore, the slope of the perpendicular line is -2.
Using the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we can plug in the values (-3, 4) and -2 to find the equation of the line: y - 4 = -2(x + 3).