Graphing the Linear Function: Y as 4 Times X

To solve this problem, we need to graph the function $Y = 4X$. Analyzing it, we recognize:

• This is a linear function in the form $Y = mX + b$, where $m = 4$ (slope) and $b = 0$ (y-intercept).
• The line passes through the origin, (0,0), because $b = 0$.
• For a slope of 4, each unit increase in $X$ results in a 4-unit increase in $Y$.

We look for a graph showing a straight line through (0,0), with slope 4, represented as a steep incline upwards along the coordinate plane.

From the provided choices, we select the graph with a linear function that passes through the origin at an angle indicating a slope of 4, leading us to choice 2, the correct representation.

Thus, the correct graph of the function $Y = 4X$ is the one depicted in choice 2.