For the equation Y = 2|X - 3| + 4, what is the y-intercept?

To determine the y-intercept of the equation Y = 2|X - 3| + 4, we need to evaluate the function when X is equal to 0. The y-intercept is defined as the point where the graph of the equation crosses the y-axis, which occurs when the value of X is zero.

Substituting X = 0 into the equation, we get:

Y = 2|0 - 3| + 4.

Calculating the absolute value, we find:

|0 - 3| = |-3| = 3.

Now we can substitute that back into the equation:

Y = 2(3) + 4,

Y = 6 + 4,

Y = 10.

Thus, the y-intercept is the point (0, 10). This indicates when X is 0, Y equals 10, confirming that the correct answer matches the coordinates given in the choice.

This approach shows how substituting the X value into the equation directly leads to the correct identification of the y-intercept.