Answer:
y = (1/2)x + 4
Explanation:
To find the equation of a line that passes through two points, (2, 5) and (6, 7), we can use the point-slope form of the equation of a line: y - y1 = m(x - x1).
Step 1: Calculate the slope (m): The slope of a line passing through two points, (x1, y1) and (x2, y2), can be found using the formula: m = (y2 - y1) / (x2 - x1). In this case, the points are (2, 5) and (6, 7). Substituting these values into the formula, we get: m = (7 - 5) / (6 - 2) = 2 / 4 = 1/2.
Step 2: Choose one point (x1, y1) and substitute it into the point-slope form: Let's choose (2, 5). Substituting these values into the point-slope form, we get: y - 5 = (1/2)(x - 2).
Step 3: Simplify the equation: To simplify, we can distribute (1/2) to both x and -2: y - 5 = (1/2)x - 1. Rearranging the equation, we have: y = (1/2)x - 1 + 5. Simplifying further, we get: y = (1/2)x + 4.
Therefore, the equation of the line that passes through the points (2, 5) and (6, 7) is y = (1/2)x + 4.