Final answer:
The standard form of the equation that passes through the point (-2, 4) and is parallel to x - 2y = 6 is y = (1/2)x + 5.
Step-by-step explanation:
To write the standard form of the equation for a line that is parallel to a given line, we need to determine the slope of the given line. The slope of the given line can be found by rearranging the equation into the form y = mx + b, where m is the slope. In this case, the given line is x - 2y = 6. Rearranging the equation gives us y = (1/2)x - 3. Now we know that the slope of the given line is 1/2. Since the line we are looking for is parallel to the given line, it will have the same slope of 1/2. So the equation we are looking for can be written in the form y = (1/2)x + b. To find b, we substitute the coordinates of the given point (-2, 4) into the equation. 4 = (1/2)(-2) + b Simplifying, we get 4 = -1 + b. Adding 1 to both sides, we get 5 = b. So the equation of the line that passes through the point (-2, 4) and is parallel to x - 2y = 6 is y = (1/2)x + 5.