Answer:
D) y = 2x + 8
Explanation:
Parallel lines are coplanar lines that never intersect.
Parallel Slopes
All parallel lines have the same relationship between their slopes. For 2 lines to be parallel, their slopes must be equal. The question tells us that the slope of the first line is 2. This means that only answer choices B and D are viable.
The slopes of answer choices A and C are perpendicular to the line given.
Testing the Answers
Both B and D could be parallel to the line given; however, we are also told that the line must pass through (-2, 4). To see which answer is correct, we can plug in the x and y-values and solve. If a line passes through a point, then the equation will be true when the values are plugged in.
Let's start with answer B.
Since this statement is not true, we know that y = 2x + 4 does not pass through the point (-2, 4).
Next, we need to test answer choice D.
This is true, so y = 2x + 8 must pass through the point (-2, 4). Since answer choice D has a parallel slope and passes through (-2, 4), it must be the correct answer.