Find the equation of a line through the coordinate (3,-2) and parallel to the line represented by y= 1/2x - 2
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A. y=1/2x + 4
B. y= -2x + 4
C. y= 1/2x - 7/2
D. y=1/2x - 5/2
Since the line we want to find the equation for is parallel to y = 1/2x - 2, the slope of the line will also be 1/2.
Therefore, the equation of the line passing through the point (3,-2) and having a slope of 1/2 can be found using the point-slope formula:
y - y1 = m(x - x1)
Substitute the values x1 = 3, y1 = -2 and m = 1/2:
y - (-2) = 1/2(x - 3)
y + 2 = 1/2x - 3/2
y = 1/2x - 3/2 - 2
y = 1/2x - 3/2 - 4/2
y = 1/2x - 7/2
Therefore, the equation of the line through the point (3,-2) and parallel to y = 1/2x - 2 is y = 1/2x - 7/2, which is option C.