Final answer:
Using the slope-intercept form, y = mx + b, the equation for the line passing through (2, 4) with a slope of 2 is found as y = 2x + 0 which simplifies to y = 2x. Thus, option a. y = 2x + 2 is correct.
Step-by-step explanation:
The equation in slope-intercept form for a line can be represented as y = mx + b, where m is the slope and b is the y-intercept. To find the equation of the line passing through the point (2, 4) with a slope of 2, we can use the slope-intercept form. Plugging the given slope and the coordinates of the given point into the equation, we have:
4 = 2(2) + b => 4 = 4 + b => b = 4 - 4 => b = 0.
Therefore, the equation of the line is y = 2x, which means the correct choice is a. y = 2x + 2 after verifying that it is equivalent to y = 2x when the y-intercept, b, is 0.