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What is the equation of the line that passes through points (3, -1) and (6, 7)?

  1. y = 4x + 5

  2. y = 4x – 5

  3. y = –4x + 5

  4. y = –4x – 5

The correct answer is: y = 4x + 5

The correct equation is y = 4x + 5. This can be found using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept. To find the slope, we use the slope formula, (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the given points. Plugging in (3, -1) and (6, 7), we get a slope of 8/3. Then, we can substitute the slope and one of the given points into the slope-intercept form to solve for b. Using (6, 7), we get 7 = (8/3)(6) + b, which simplifies to b = 5. Therefore, the