Final answer:
After calculating the slope of line m to be 3/2 using the points (2, -7) and (4, -4), we can conclude that none of the provided options have the same slope, and therefore, none of the lines are parallel to line m.
Step-by-step explanation:
The question involves determining which line is parallel to a given line m. To find a line that is parallel to line m, we must first calculate the slope of line m.
We can use the points (2, -7) and (4, -4) to find the slope of line m using the formula slope (m) = (y2 - y1) / (x2 - x1). Substituting the given points, we get m = (-4 + 7) / (4 - 2) = 3 / 2. Therefore, the slope of line m is 3/2.
Now we look for the line with the same slope among the options provided:
- A. y = -x + 2 has a slope of -1,
- B. y = x - 9 has a slope of 1,
- C. x = 5 does not represent the slope-intercept form of a line, it's a vertical line, and
- D. y = -1 is a horizontal line with a slope of 0.
Since none of the equations listed have the same slope as line m (3/2), none of the given lines are parallel to line m.