Find the equation of a line through the coordinate (3,-2) and parallel to the line represented by y=1/2x-2.
A. y=1/2x+4
B. y=-2x+4
C. y=1/2x-7/2
D. y=1/2x-5/2
.
The given line has a slope of 1/2. Since we want a line parallel to this, it will also have a slope of 1/2.
Using the point-slope form of a linear equation, we have:
y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Plugging in the values, we have:
y - (-2) = 1/2(x - 3)
y + 2 = 1/2x - 3/2
Subtracting 2 from both sides, we get:
y = 1/2x - 7/2
Therefore, the equation of the line through the coordinate (3,-2) and parallel to the line y=1/2x-2 is y = 1/2x - 7/2, which is option C.