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Find the equation of the line passing through the point (1, -2) and parallel to the line x - 2y = 6.

a) 2x - y = 3
b) 2x + y = 4
c) x + 2y = -2
d) 3x - 2y = 5

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Final answer:

To find the equation of a line parallel to another line, determine the slope of the given line, and then use the point-slope form of a linear equation to find the equation of the parallel line.

Step-by-step explanation:

To find the equation of a line parallel to another line, we need to first determine the slope of the given line, and then use the point-slope form of a linear equation to find the equation of the parallel line.

The given line is x - 2y = 6.

To find the slope of this line, we can rewrite the equation in slope-intercept form y = mx + b, where m is the slope. Rewrite the equation as -2y = -x + 6, then divide by -2 to get y = 0.5x - 3.

Since the parallel line has the same slope, the equation of the parallel line is y = 0.5x + b, where b is the y-intercept. We can substitute the coordinates of the given point (1, -2) into this equation to find b.

-2 = 0.5(1) + b

-2 = 0.5 + b

b = -2 - 0.5

b = -2.5

Therefore, the equation of the line passing through the point (1, -2) and parallel to the line x - 2y = 6 is y = 0.5x - 2.5.

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