Final answer:
The two lines represented by y = x - 4 and y = 3x + 4 are not parallel, as their slopes are different. They intersect at the point (-4, -8), which can be found by solving the equations simultaneously.
Step-by-step explanation:
The question pertains to determining whether two lines are paralle or if they intersect, and if they intersect, finding their point of intersection. The equations provided for Line A and Line B are Line A: y = x - 4 and Line B: y = 3x + 4. To determine if the lines are parallel, we must compare their slopes. The slope of Line A, which is the coefficient of x, is 1 while the slope of Line B is 3. Because the slopes are not equal, we conclude that the lines are not parallel and will intersect at exactly one point.
To find the point of intersection, we set the y-values of both equations equal to each other since at the point of intersection, both lines will have the same x and y values. This gives us x - 4 = 3x + 4. Solving this equation for x, we subtract x from both sides to get -4 = 2x + 4, and then subtract 4 from both sides to get -8 = 2x. Dividing both sides by 2 gives us x = -4. We can then substitute x = -4 into either of the original equations to find the corresponding y value. If we substitute it into Line A's equation, we get y = (-4) - 4 which simplifies to y = -8. Thus, the point of intersection of Line A and Line B is (-4, -8).