The point-slope form of the equation of a line is given by the following expression:
y - y1 = m(x - x1)
Where m is the slope of the line and (x1, y1) is a point where the line passes through.
The slope of the line can be determined with the following formula:
Where (x1, y1) and (x2, y2) are two points where the line passes through. In this case we are told that the line passes through the points (-2,-6) and (6,5). By replacing the x and y coordinates of these points into the formula of the slope, taking x1 as -2, x2 as 6, y1 as -6 and y2 as 5, we get:
Then, the slope of the line equals 11/8, by replacing 11/8 for m into the slope-point form, we get:
y - y1 = 11/8(x - x1)
By taking one of the points, for example (-2,-6), we replace the x and y-coordinates that appear in the equation of the line, to get:
y - (-6) = 11/8(x - (-2))
y + 6 = 11/8 (x + 2)
Then, the equation of the line in slope-point form is y + 6 = 11/8 (x + 2)