For any line passing through the points (x1,y1) and (x2,y2), its slope is given by:
a = (y2 - y1)/(x2 - x1)
And its intercept is given by:
b = y1 - ax1 = y2 - ax2
And the equation of this line, in the slope-intercept form, is y = ax + b
Then, for a line passing through the points (3,4) and (-6,5), we have:
a = (5 - 4)/(-6 - 3) = -1/9
Then, the intercept is:
b = 4 + 3/9 = 13/3
Therefore, the equation of the line is given by:
y = -x/9 + 13/3