Which of the following is a point-slope equation of a line that passes through
the points (5,2) and (-1,-6)?
O A. y-2-(X-5)
O B. y-2--x-5)
O C. y-2--|(x-5
OD. y-2-(x-5)

To find the equation in point-slope of a line passing through two points, we can use the formula: [tex]y - y₁ = m(x - x₁)[/tex] Where (x₁, y₁) are the coordinates of one point, m is the slope of the line, and (x, y) are the coordinates of any other point on the line and  [tex]y-2-(x-5)[/tex] Therefore the correct option is D.

Given that the two points are (5,2) and (-1,-6), we can substitute these values into the formula: [tex]y - 2 = m(x - 5)[/tex](using point 1: ([tex]5,2)) y + 6 = m(x + 1[/tex]) (using point 2: (-1,-6)) Now, let's simplify the equation: y = mx - 5m + 2 (equation 1) y = mx + m - 6 (equation 2) From equations 1 and 2, we can determine that the expected point-slope equation will have the form y - 2 = m(x - 5),

which matches option D. Therefore, the correct point-slope equation of the line passing through the points (5,2) and (-1,-6) is: y - 2 = m(x - 5)

Hence the correct option is D

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