Final answer:
The new equation after translating the original line y = -2x + 3 along the vector (2,4) is y = -2x + 7.
Step-by-step explanation:
The student is asking about the equation of a line given the original line y = -2x + 3 and its domain.
The new equation needs to be found based on translating the line along the vector (2,4).
To determine the new equation, we take the original equation and add the components of the vector to the respective variables.
So, the translation would result in adding 2 to the x-coordinate and 4 to the y-coordinate, yielding the formula y = -2(x-2) + (3+4).
Simplifying the equation, we get y = -2x + 7.
This new equation has the same slope as the original equation, which maintains the parallelism between the two lines due to the translation.