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.