For a couple of minutes I want you to think about first
That flat horizontal line has zero slope. There's no change in y for every unit change in x.
The answer is A.
Parallel lines have the same slope, which is 1/2 in this problem. The equation of the line in A matches the slope of 1/2 and also passes through (-8,0). You can check that it does by substituting the x and y values in the equation, like this:
0 = 1/2(-8) + 4
0 = -4 +4
0 = 0 which checks!
Answer: The first one is "translated 4 units down". The second one is "vertically stretched by a factor of 4".
Recall that y = f(x). When we say f(x)-4, we really mean y-4 so that means each y coordinate of all the points on the graph have been reduced by 4. Visually this shifts the graph down 4 units. A translation in geometry is the technical term for shifting.
When we say 4*f(x), we are multiplying each y coordinate by 4. A point like (1,2) turns into (1,8) for instance. If you apply this to every point on the graph, then the curve is stretched vertically to be 4 times taller than it usually is; which is an informal way of saying "vertically stretched by a factor of 4"
