First, we need to determine the slope of the line. The formula for find the slope of a line is:
#m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))#
Where #(color(blue)(x_1), color(blue)(y_1))# and #(color(red)(x_2), color(red)(y_2))# are two points on the line.
Substituting the values from the points in the problem gives:
#m = (color(red)(-6) - color(blue)(7))/(color(red)(5) - color(blue)(-7)) = (color(red)(-6) - color(blue)(7))/(color(red)(5) + color(blue)(7)) = -13/12#
The point-slope form of a linear equation is: #(y - color(blue)(y_1)) = color(red)(m)(x - color(blue)(x_1))#
Where #(color(blue)(x_1), color(blue)(y_1))# is a point on the line and #color(red)(m)# is the slope.
Substituting the slope we calculated and the values from the first point in the problem gives:
#(y - color(blue)(7)) = color(red)(-13/12)(x - color(blue)(-7))#
#(y - color(blue)(7)) = color(red)(-13/12)(x + color(blue)(7))#
We can also substitute the slope we calculated and the values from the second point in the problem giving:
#(y - color(blue)(-6)) = color(red)(-13/12)(x - color(blue)(5))#
#(y + color(blue)(6)) = color(red)(-13/12)(x - color(blue)(5))#
