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 line represented by y = 1/2x - 2 has a slope of 1/2.
A line that is parallel to this line will also have a slope of 1/2.
Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we can plug in the values:
y - (-2) = (1/2)(x - 3)
Simplifying this equation:
y + 2 = (1/2)x - 3/2
Subtracting 2 from both sides:
y = (1/2)x - 3/2 - 2
Finding a common denominator:
y = (1/2)x - 3/2 - 4/2
Simplifying further:
y = (1/2)x - 7/2
Therefore, the equation of the line through the coordinate (3, -2) and parallel to y = 1/2x - 2 is y = (1/2)x - 7/2.
The correct option is C.