Final answer:
To find the equation of a line parallel to a given line and passing through (2, 3), first determine the slope of the given line. Then, identify the equation with the same slope and check if it yields the correct y-value when x is 2. The correct equation will match this criteria.
Step-by-step explanation:
The task is to find the equation of a line that is parallel to a given line and passes through a specific point, which in this case is (2, 3). If two lines are parallel, they must have the same slope. We start by identifying the slope of the given line, which is based on the standard form of a linear equation, y = mx + b, where m is the slope. Assuming the given line falls into the standard form, then we just need to ensure that the slope of the new line is the same.
From the provided options, we can see:
- Option A: x + 2y = 4 can be rearranged to 2y = -x + 4, which gives us y = -1/2x + 2, so the slope is -1/2.
- Option B: x + 2y = 8 is similar to option A and also has a slope of -1/2 when put in slope-intercept form.
- Options C and D: 2x + y = 4 and 2x + y = 8 can be rearranged to y = -2x + 4 and y = -2x + 8, respectively, both with a slope of -2.
To find the correct option, we must first determine the slope of the given line and then match it with one of the options provided that passes through the point (2, 3). The correct equation will have the same slope as the given line and yield a y-value of 3 when x is 2.