Final answer:
The equation of the line passing through the point (-2, 5) and parallel to the line x + 2y - 6 = 0 is y = (-1/2)x + 4. This is found by using the same slope of the given line, which is -1/2, and applying the point-slope form with the given point.
Step-by-step explanation:
The question asks us to determine the equation of a straight line that passes through the point (-2;5) and is parallel to the line given by the equation x + 2y - 6 = 0. To find the equation of the line parallel to the given line, we need to use the same slope. The slope of the given line can be found by rearranging the equation into slope-intercept form (y = mx + b), which in this case will be 2y = -x + 6 or y = (-1/2)x + 3. Hence, the slope (m) of the given line is -1/2. A line parallel to this must also have a slope of -1/2.
Using the point-slope form of a line's equation, which is y - y1 = m(x - x1) where m is the slope and (x1, y1) is a point on the line, we plug in our point (-2, 5) and slope (-1/2) to get:
y - 5 = (-1/2)(x - (-2))
Now we simplify this to get the equation of the line in slope-intercept form:
y - 5 = (-1/2)x - 1y = (-1/2)x + 4
This is the equation of the line passing through (-2;5) that is parallel to the line x + 2y - 6 = 0.