Final answer:
The equation of the line that is perpendicular to the line y = (1/2)x - 9 and passes through the point (7, 10) is y = -2x + 24.
Step-by-step explanation:
To write the equation of the line that is perpendicular to the line y = (1/2)x - 9 and passes through the point (7, 10), first, we need to determine the slope of the given line. The slope of the line given by y = (1/2)x - 9 is 1/2. Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of the line we want to find is -2 (the negative reciprocal of 1/2).
Next, we use the point-slope form of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a given point on the line. Substituting the slope -2 and the point (7, 10), the equation becomes:
y - 10 = -2(x - 7)
Fully expanding and simplifying, the equation is then:
y - 10 = -2x + 14
y = -2x + 24
Therefore, the equation of the line that is perpendicular to y = (1/2)x - 9 and passes through the point (7, 10) is y = -2x + 24.