Final answer:
The equation y = 4(x+2) translates the original line y = 4x by 2 units to the left, indicating a horizontal shift in the negative x-direction. So, the correct answer is: b) 2 units to the left
Step-by-step explanation:
The question asks By how much does (y = 4(x+2)) translate the line (y = 4x) horizontally? This involves understanding horizontal transformations of linear functions in the form of y = mx + b, where m is the slope and b is the y-intercept. The original equation y = 4x has no horizontal translation since the x is not being added or subtracted inside the parentheses. However, the equation y = 4(x+2) has a plus 2 within the parentheses, which affects the x-term. In the context of transformations, adding a number to x inside the parentheses shifts the graph to the left by that number of units. Therefore, the equation y = 4(x+2) translates the line y = 4x 2 units to the left, which corresponds to option b) 2 units to the left.