Final answer:
To find the equation of the linear line that passes through the given points, calculate the slope and then use one of the points to find the equation using point-slope form. The correct equation based on the calculations is x - 2y = -8, which does not match any of the provided multiple-choice options, indicating a potential error in the question.
Step-by-step explanation:
To find the equation of the line that passes through the points (2, 5) and (6, 7), we first need to determine its slope (m). The slope of a line through two points (x1, y1) and (x2, y2) is given by the formula m = (y2 - y1) / (x2 - x1). Substituting our points into this formula, we get m = (7 - 5) / (6 - 2) = 2 / 4 = 1/2.
We then use the point-slope form of a linear equation, y - y1 = m(x - x1), and substitute one of the points and the slope to find the equation. Let's use the point (2, 5): y - 5 = 1/2(x - 2). Now, we'll simplify this to the slope-intercept form, y = mx + b. Multiplying both sides by 2 and then simplifying gives us 2y - 10 = x - 2, and then moving terms around yields x - 2y = -8.
By looking at the multiple choice options, we need to express this equation in the form y = mx + b or something that can be rearranged to that form. The correct equation must be equivalent to x - 2y = -8. The answer is not listed in the provided options; therefore, there could be an error in the question or the answer choices.