What is the equation of a line that passes through the points (2,3) and (4,5)?
Correct: A
To find the equation of the line, we first need to find the slope (m) of the line. The formula for slope is m = (y2 - y1) / (x2 - x1), where (x1, y1) = (2, 3) and (x2, y2) = (4, 5). Substituting these values gives m = (5 - 3) / (4 - 2) = 2 / 2 = 1. Now that we have the slope, we can use the point-slope form of the line equation, y - y1 = m(x - x1), and substitute m = 1 and (x1, y1) = (2, 3) to get y - 3 = 1(x - 2), which simplifies to y - 3 = x - 2. Adding 3 to both sides gives y = x + 1.