First, determine the slope. The slope can be found by using the formula: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))#
Where #m# is the slope and (#color(blue)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the two points on the line.
Substituting the values from the points in the problem gives:
#m = (color(red)(8) - color(blue)(8))/(color(red)(4) - color(blue)(-6))#
#m = (color(red)(8) - color(blue)(8))/(color(red)(4) + color(blue)(6))#
#m = 0/10 = 0#
The point-slope formula states: #(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))#
Where #color(blue)(m)# is the slope and #color(red)(((x_1, y_1)))# is a point the line passes through.
Substituting the slope and values from the first point gives:
#(y - color(red)(8)) = color(blue)(0)(x - color(red)(-6))#
#(y - color(red)(8)) = color(blue)(0)(x + color(red)(6))#
We can also substitute the slope and values from the second point giving:
#(y - color(red)(8)) = color(blue)(0)(x - color(red)(4))#
