Final answer:
Without the graphs, it's not possible to determine which graph (A-D) represents the equation y=4⋅2x. Nevertheless, the y-intercept can be determined to be 4 by evaluating the equation at x=0.
Step-by-step explanation:
The correct representation of the equation y=4⋅2x and its y-intercept cannot be determined without seeing the actual graphs labeled A through D. However, we can explore the properties of the equation to understand what the graph should look like and determine its y-intercept. The given equation is in the form y=abx, which is an exponential function, not a linear one. The base of the exponential, b, is 2, which is greater than 1, so the graph will show exponential growth. The coefficient, a, represents the y-intercept because it is the value of y when x=0. Therefore, by evaluating the equation at x=0, we find the y-intercept is 4.
To determine which graph represents the equation and to find the correct y-intercept, we must look for a graph with an exponential curve starting at a y-intercept of 4. The y-intercept can be found by substituting x with 0 in the equation: y=4⋅20 = 4⋅1 = 4. So the y-intercept is (0, 4).